Acceleration of laser ray tracing simulations of additive manufacturing microstructures

Abstract

A method and system for accelerating digital twin simulations of energy-beam additive manufacturing by replacing repeated laser ray tracing with a trained surrogate while preserving physical admissibility and simulation stability. For a build region discretized on a three-dimensional grid, a material-distribution field representing an evolving metal–gas interface and a temperature field are provided to a trained three-dimensional neural network that outputs a predicted absorbed energy deposition field. An interface mask derived from the material-distribution field restricts deposition to physically valid interface locations, and a conservation constraint maintains consistency of total absorbed energy. The physically admissible deposition field is coupled as a heat-source term into a time-stepping multiphysics solver to update thermal fields and predict melt pool evolution. In further embodiments, predicted thermal histories are used to predict microstructure descriptors and / or distortion metrics, enabling efficient evaluation and optimization of printer instructions across complex geometries and process conditions.

Description

ACCELERATION OF LASER RAY TRACING SIMULATIONS OF ADDITIVE MANUFACTURING MICROSTRUCTURES STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

[0001] This invention was made with Government support under Contract No. DE-AC52-07NA27344 awarded by the United States Department of Energy. The Government has certain rights in the invention.CROSS REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. provisional application no 67 / 765,300 filed on February 28, 2025 which is incorporated by reference as if fully set forth.BACKGROUND

[0002] A technology field that continues to grow in relevance with expanding capabilities is additive manufacturing (AM) or 3D printing. AM encompasses a large family of technologies, such as laser powder bed fusion (LPBF) and directed laser energy deposition (DED), where parts are manufactured layer by layer according to a set of printer instructions e.g., a computer aided design (CAD) file, upon melting and rapid solidification of powder in a layer.

[0003] One of the major challenges for maturing AM technologies is optimizing the process parameters, such as laser power and scan speed, to meet manufacturing requirements. Leveraging experimental and / or simulation data will be an instrumental approach to solving the AM challenge. Simulation data creates digital twins, or digital replicas that model the full-scale complexity of an actual physical process. One means of generating a digital twin is via complex physics simulation modelling engines such as ALE3D, FLOW3D, Ansys, or Abaqus. Running physics engines at the requisite level to generate reliable digital twins is a computationally intensive process that is very time consuming and requires a tremendous amount of compute power.

[0004] ALE3D-4i, or in short ALE3D, is a multiphysics code developed at Lawrence Livermore National Laboratory. In the examples disclosed herein, ALE3D was used in modeling LPBF process at the fine micrometer scale. Its predictivity has been extensively validated against experiments. It should be noted, however, that other software packages or codes may be used for modeling the disclosed processes.19596161.1SUMMARY OF THE INVENTION

[0005] The present disclosure relates to computational methods and systems for accelerating physics-based simulation workflows used to predict process outcomes in additive manufacturing, particularly in laser-based processes in which absorbed energy deposition depends strongly on evolving surface geometry, multi-reflection, and shadowing. A recurring technical problem in such workflows is that high-fidelity laser energy-deposition models, such as laser ray tracing, are computationally expensive and can dominate wall-clock time when coupled to multiphysics solvers that also compute transient temperature, melt pool evolution, and solidification behavior. This computational burden makes it impractical to perform sufficiently large domains, long build times, or repeated parameter sweeps needed for process development, qualification, and optimization of printer instructions. A related technical problem is that downstream predictions of microstructure evolution and distortion / residual-stress-driven shape change can be similarly expensive when modeled with high-fidelity physics formulations, thereby limiting the practical use of digital twins for iterative design and manufacturing planning.

[0006] Embodiments of the inventions provide technical solutions that substantially reduce computational cost while maintaining fidelity needed for predictive simulation. In one class of embodiments, a trained machine learning model is used as a surrogate for a laser ray tracing solver to predict an absorbed energy deposition field. The surrogate is configured to accept as input at least a representation of material distribution and geometry (for example, a metal volume fraction field that encodes the evolving interface) and a representation of thermal state (for example, a temperature field), and to output a three-dimensional absorbed energy deposition field on a computational grid. The surrogate may be implemented as a three-dimensional fully convolutional network, including encoder-decoder architectures with skip connections and parameter-efficient convolution modules that reduce memory footprint while preserving the ability to represent non-local optical effects. This surrogate replaces repeated ray tracing calls during a coupled time-stepping simulation, thereby reducing the dominant computational bottleneck and enabling faster evaluation of process conditions and toolpaths.

[0007] To address the technical challenge that deposition physics in laser-based additive manufacturing is concentrated at metal-gas interfaces and that global absorbed energy must remain consistent with beam power and coupling assumptions to preserve stability of the coupled simulation, certain embodiments apply interface-aware 29596161.1constraints during training and inference. In these embodiments, an interface mask derived from the material distribution field is used to focus supervision on voxels corresponding to the physical deposition support, and to suppress non-physical deposition predictions away from the interface during inference. In addition, a global constraint term is incorporated into the training objective to enforce conservation of absorbed energy, reducing drift in total absorbed power that can otherwise accumulate across timesteps and destabilize the thermal evolution. In further embodiments, preprocessing operations are applied to training targets to mitigate discretization and sampling artifacts inherent in ray-based methods, while preserving physically meaningful features such as shadowed regions and multi-reflection hot spots.

[0008] In another class of embodiments, the accelerated energy deposition predictions are used as part of an end-to-end digital twin pipeline that predicts microstructure evolution. A technical problem addressed by these embodiments is that microstructure simulation, including solidification front tracking and grain growth, can be computationally expensive and difficult to run at part scale or across many candidate process plans. In certain embodiments, a second trained model predicts mi era structure descriptors using thermal fields and / or thermal history features produced by the coupled simulation. The microstructure model may be implemented using graph-based neural networks, message passing, or other architectures suited to representing evolving neighborhoods and state transitions, and may output microstructure fields such as phase / state (liquid / mushy / solid), grain identifiers, orientation descriptors, growth kinetics parameters, and / or melt pool geometry descriptors derived from predicted thermal evolution. In some embodiments, the microstructure model performs single-step prediction that is iterated autoregressively to obtain time evolution, enabling accelerated simulation of microstructure development over multiple timesteps and layers.

[0009] Embodiments further address the technical problem that prediction of distortion and dimensional deviation due to residual stress and thermo-mechanical response can be prohibitively expensive when performed with full thermo-mechanical simulation for many candidate builds. In certain embodiments, distortion is predicted using a reduced-order modeling pathway that compresses high-dimensional simulation fields into a low-dimensional latent representation and then performs fast regression from that latent representation and / or process descriptors to distortion outputs. In some embodiments, a graph convolutional autoencoder is trained to encode and reconstruct distortion-relevant fields, and a regression model such as Gaussian process regression is trained to predict distortion outputs or latent variables, optionally providing uncertainty 39596161.1estimates. This reduced-order pathway enables rapid estimation of displacement fields, surface deviation metrics, warpage measures, or other dimensional-error indicators suitable for screening and optimization.

[0010] In various embodiments, the disclosed techniques are integrated into a practical computing workflow that receives printer instructions and associated process parameters, predicts absorbed energy deposition in a time-stepping simulation using the trained surrogate in place of repeated ray tracing, and produces one or more predicted outcomes including thermal fields, melt pool descriptors, microstructure descriptors, and / or distortion metrics. In certain embodiments, these predicted outcomes are used to evaluate candidate printer instructions prior to printing, to identify process windows that satisfy target criteria, and to modify printer instructions to reduce predicted defects, achieve target micro structure, and / or reduce distortion. In some embodiments, the system supports repeated evaluation across large parameter spaces because inference time of the surrogate is substantially less sensitive to geometric complexity than ray tracing runtime, thereby enabling exploration of complex parts, re-entrant geometries, and rough interfaces that would otherwise be computationally prohibitive.

[0011] In certain embodiments, reliability under domain shift is improved through runtime safeguards. For example, some embodiments compute a confidence or consistency measure associated with surrogate predictions, including measures derived from energy conservation checks and / or indicators of geometric novelty, and selectively invoke higher-fidelity simulation for particular timesteps or regions when the confidence measure indicates elevated risk. Some embodiments store such high-fidelity results for subsequent retraining or fine-tuning, providing a path to incremental improvement of the surrogate as new geometries and process conditions are encountered.

[0012] Accordingly, embodiments of the inventions solve the technical problems of excessive computational cost and limited scalability in high-fidelity additive manufacturing simulations by replacing or accelerating ray tracing with a physically constrained surrogate model, by providing accelerated microstructure prediction models that leverage the resulting thermal histories, and by providing reduced-order distortion prediction pathways that enable rapid dimensional outcome estimation. These technical solutions improve the feasibility of predictive digital twins for process development, qualification, and optimization by enabling substantially faster simulations while preserving the physical constraints and outcome fidelity required for practical use.49596161.1LLNL-077518-8097. WG00BRIEF DESCRIPTION OF THE DRAWINGS

[0013] FIG. 1 is a block diagram of a neural network architecture.

[0014] FIG. 2 is a diagram of a DED AM printer.

[0015] FIG. 3 is a flow diagram illustrating training a neural network.

[0016] FIG. 4 is a flow diagram of modification of additive manufacturing printer instructions.

[0017] FIG. 5 is a block diagram illustrating an example machine learning (ML) system, in accordance with one or more embodiments.

[0018] FIG. 6 is a block diagram illustrating an example computer system, in accordance with one or more embodiments.DETAILED DESCRIPTION

[0019] Use of a workpiece digital twin of the result of AM printer instructions enables previsualizations, tests, and revisions to the AM printer instructions before physically printing a workpiece. Generating the physical workpiece requires time, uses printer production bandwidth, and, in some cases, consumes expensive printer materials (e.g., specialized alloys). A workpiece digital twin enables microstructure examination and testing and enables identification of printer instruction errors. Where errors or structural insufficiency are identified, a user implements printer instruction revisions. Generation of digital twins has been performed with complex physics simulations such as laser ray tracing. Such simulations are very time consuming and limit feasibility of AM printers for high end applications.

[0020] Accelerating complex physics simulations using deep learning is a pathway to creating digital twins as users need to be able to achieve predictions faster than running the physics process itself. In the case of AM, the goal is to rely on computational optimization rather than Edison’s experimental trial and error approach, i.e. 3D printing exemplar models using a wide process parameter sweeps and picking optimal parameters using postmortem analysis. This costs time and money and prevents wide adoption of AM technologies. Disclosed herein are implementations of deep learning U-net architecture that provide advantage over the expensive physics of laser ray tracing that is used in predictive high-fidelity simulations that couple thermal and fluid dynamics to model laser melting and material solidification.

[0021] Cheaper simulations are often less predictive partly because they sacrifice the heat source physics with calibrated heat sources. AM technologies are driven by laser energy being absorbed in specific amounts by the material. The amount of energy 59596161.1LLNL-077518-8097. WOOOabsorbed depends on the type of material, on surface topology and temperature. For instance, some metallic materials like copper and aluminum are more reflective than titanium-based alloys such as Ti-6AI-4V, hence a lot of incoming laser energy is not absorbed, i.e. wasted. Meanwhile, adding powder onto a build surface (such as in LPBF) or having a deep surface depression under the laser that develops due to material evaporation, can raise the laser energy absorption (ratio of applied laser power over laser power reflected away from the work surface). The change in absorption is because upon each laser ray reflection off a surface, an amount of laser energy gets deposited. By trapping the laser rays in a volume with large surface to volume ratio, the incoming rays will lose more of their energy content upon successive reflection events, hence increasing the laser absorption value. Capturing the energy budget in the AM process is essential for accurate physics predictions.The act of modeling the process of melting by selecting the laser power influences the melting process and the generated microstructure. Knowledge of how to control the process to control the micro structure allows control of the manufactured part properties. Being able to quickly obtain the proper model helps to cut down on cost of performing actual experiments.

[0022] Some example uses of the disclosed technology include incorporating the neural network model into a multiphysics code to help accelerate modeling of laser energy deposition (laser ray tracing) and solidification micro structure evolution. The model decreases the computational cost of running all the cycles in a simulation, while maintaining same high fidelity and accuracy. A first neural network is trained to predict accurate laser energy deposition. The energy deposition field can be used in a code to heat and melt a material at each time step, without running the expensive code associated with laser ray tracing. Also, as the material solidifies, the final microstructure can be predicted using a second neural network (NN).

[0023] In some embodiments, the first NN is a computer vision model that generates a prediction of a laser energy deposition fields. Example models are fully-in memory models such as Squeezenet described in “SqueezeNet: AlexNet-level accuracy with 50x fewer parameters and <0.5MB model size” by Forrest N. landola, Song Han, Matthew W. Moskewicz, Khalid Ashraf, William J. Dally, Kurt Keutzer. In some embodiments, the second NN that generates the predictive microstructure of at least the portion of the workpiece based on the laser energy deposition field as simulated upon the additive manufacture printer instructions via a mesh-based simulation. Example mesh-based simulation models include graph neural network code by T. Pfaff, M.69596161.1LLNL-077518-8097. WG00Fortunato, A. Sanchez-Gonzalez, and P. W. Battaglia available at the time of filing of this application at Cornell University’s arXiv distribution service.

[0024] In some embodiments, training data for the first and second NN is produced by ALE3D simulations with laser ray tracing using laboratory library called LRT. In some embodiments, the second, microstructure model is trained via ALE3D-CAFE (cellular automata finite element) simulations. The core component of the models we built rely on what data we used to build the models.

[0025] In various embodiments, the systems and methods described herein are configured to predict, estimate, or otherwise determine a “microstructure” of an additively manufactured workpiece at one or more locations, times, layers, or build stages. As used herein, “microstructure” refers to one or more spatially varying descriptors of the material state that are determinative of mechanical and functional performance, and that arise from thermal history, solidification kinetics, and subsequent phase transformation. Microstructure may be represented as one or more fields defined on a voxel grid, finite element mesh, point cloud, graph, or other discretization of a build region, and may be output as full-field predictions, region-of-interest predictions, and / or summary metrics.

[0026] In certain embodiments, the microstructure representation comprises a discrete or categorical state field that indicates whether a location is liquid, mushy, or solid at a given time step, optionally accompanied by a continuous phase fraction field such as liquid fraction, solid fraction, or an order parameter that varies continuously between liquid and solid. In some embodiments, the order parameter field is denoted <|) and is defined such that ( assumes values near a first limit corresponding to one phase and values near a second limit corresponding to another phase, with intermediate values corresponding to a diffuse interface or mushy region. The order parameter field may be produced by a physics simulation, such as a phase-field or phase-field-like formulation, or by an equivalent representation produced by a coupled cellular automaton I finite element approach or other solidification model. In these embodiments, the micro structure prediction may include one or more snapshots of <J> at selected times, may include a time series of < values, or may include features derived from <[), such as interface location, interface thickness, or the boundary of a melt pool.

[0027] In certain embodiments, the microstructure representation comprises a grain structure description. Grain structure may be represented by a grain identifier field in which each location is associated with an integer or label indicating membership in a particular grain. Grain structure may further include a crystallographic orientation field associated with each grain identifier, such as Euler angles, Rodrigues parameters, an 79596161.1LLNL-077518-8097. WOOOorientation matrix, a quaternion representation, ora vector representation of a preferred growth direction. Grain structure may also include grain size metrics, grain boundary area density, grain aspect ratio, and texture metrics computed over a region. In some embodiments, the system outputs one or more maps that visually depict grain identifiers and / or orientation, for example by assigning distinct colors to grain labels and / or by encoding orientation in a color scheme. In certain embodiments, the microstructure outputs are provided for a two-dimensional section (e.g., a slice plane) of the build region for visualization and inspection, and in other embodiments the outputs are provided in three dimensions.

[0028] In certain embodiments, microstructure is represented by one or more cellular automaton state variables and / or quantities used by a cellular automaton or cellular automaton finite element formulation for solidification and grain growth. Such variables may include, without limitation, a cell state variable (e.g., liquid / mushy / solid), a nucleation indicator, a growth direction indicator, a local solid fraction, and one or more quantities associated with a growth geometry. In some embodiments, the growth geometry is modeled by an octahedral growth construct, and the microstructure state includes a descriptor of octahedron size, an octahedron lifetime, a time-to-capture value, or other growth kinetics parameters. In these embodiments, microstructure prediction may include predicting a next-step cellular automaton state for each cell, predicting one or more growth kinetics values that govern how a grain expands into neighboring cells, and predicting one or more neighbor-capture outcomes that identify which neighboring cells are captured or transformed at a subsequent time. In certain embodiments, these predicted quantities are used to advance a microstructure simulation forward in time at reduced computational cost, thereby producing an evolving microstructure consistent with the thermal conditions.

[0029] In certain embodiments, microstructure outputs include melt pool geometry descriptors. Melt pool descriptors may include a melt pool boundary or contour, melt pool depth, melt pool width, melt pool length, melt pool volume, and / or the location of a solidification front. These descriptors may be derived from a temperature field relative to a melting temperature, derived from the order parameter field, derived from predicted phase fraction, or directly predicted as outputs. In some embodiments, the melt pool boundary is represented as an isosurface of afield (e.g., a temperature threshold or order parameter threshold) and may be provided as a triangulated mesh, contour line(s), or voxelized boundary mask. Melt pool descriptors are treated as part of “predictive microstructure” because they strongly govern solidification rates, epitaxial growth, and 89596161.1grain morphology.

[0030] In certain embodiments, micro structure outputs include one or more defect or quality proxies that are microstructure-adjacent, such as a porosity proxy, lack-of-fusion proxy, keyhole risk proxy, or spatter / plume attenuation proxy. These proxies may be computed from predicted energy deposition and thermal history, and / or may be predicted directly as fields. For example, regions with insufficient predicted absorbed energy deposition at or near a powder-solid interface may be labeled as at-risk for lack-of-fusion, while regions with extreme energy density and temperature gradients may be labeled as at-risk for keyhole formation. In some embodiments, the system outputs a scalar quality score or risk probability for each voxel, cell, or region of interest, which can be used in optimization or qualification workflows.

[0031] In various embodiments, the microstructure outputs described above are produced by one or more trained machine learning models that emulate or accelerate a physics simulation. In certain embodiments, a first trained model predicts absorbed energy deposition for a laser-based additive process, thereby replacing or accelerating a ray tracing simulation that would otherwise account for reflection, absorption, and multiple interactions of laser rays with an evolving interface. The predicted absorbed energy deposition is used to update or drive a temperature field in a thermal simulation, and the temperature field and / or derived thermal history features are then used by a second trained model to predict microstructure evolution. This two-stage pipeline is advantageous because microstructure is sensitive to thermal gradients and cooling rates, and because high-fidelity ray tracing and microstructure simulation are both computationally expensive.

[0032] In certain embodiments, the microstructure model receives as input a representation of the local state of the workpiece and / or powder bed including, without limitation, a temperature field, a metal volume fraction field, an interface mask identifying the powder-solid or solid-gas interface, one or more thermal history features (peak temperature, time above melt, cooling rate proxy, thermal gradient magnitude), and optionally one or more prior microstructure states. The input may be provided on a voxel grid for convolutional processing, or on a graph for message passing processing. When the microstructure model operates on a graph, nodes may represent cells, voxels, mesh elements, or other spatial units, and edges may represent adjacency or neighborhood relationships. Node features may include the fields and derived features described above, and the model outputs may include the next microstructure state at each node and / or one or more continuous growth parameters.99596161.1

[0033] In some embodiments, the microstructure model is trained to perform single-step prediction, where the model predicts the microstructure state at a next time step given the micro structure state at a current time step. The model is then iterated autoregressively to generate a sequence of microstructure states across a layer or across multiple layers. In some embodiments, training includes teacher forcing in which groundtruth microstructure states from simulation are intermittently provided during training to stabilize multi-step rollout, while inference uses the model’s own predictions. In certain embodiments, stability constraints are applied during rollout, such as enforcing that solid fraction remains between zero and one, enforcing that phase transitions occur only in physically plausible directions over a time increment, and enforcing that grain capture rules are consistent with the predicted growth geometry.

[0034] In certain embodiments, microstructure is output at multiple resolutions to balance speed and fidelity. For example, a coarse-resolution prediction may be generated for a full build region, while fine-resolution predictions are generated for regions of interest such as overhangs, thin walls, scan track overlaps, or areas with high predicted thermal gradients. In some embodiments, the system uses an adaptive discretization such as an octree, where microstructure predictions are refined near the melt pool boundary or near interfaces. In such embodiments, microstructure fields predicted at different resolutions may be reconciled via interpolation, conservative remapping, and / or boundary consistency constraints so that transitions between resolutions do not create artifacts in predicted grain structure or phase fields.

[0035] In some embodiments, micro structure outputs are accompanied by summary metrics and visualizations useful for process planning. Summary metrics may include predicted grain size distribution, texture metrics, orientation distribution functions, solidification front velocity proxies, and spatial maps of defect risk proxies. Visualizations may include two-dimensional slices through predicted three-dimensional grain identifier fields, orientation maps, phase fraction maps, and melt pool boundary overlays. In certain embodiments, these outputs are used to evaluate candidate printer instructions prior to printing, including selecting scan parameters and scan ordering strategies that promote a target microstructure, reduce defect risk, or balance competing objectives such as build time and performance.

[0036] In certain embodiments, the definition of “microstructure” and the selected microstructure outputs are dependent on a target application. For example, for fatigue-critical components, grain size, texture, and lack-of-fusion risk proxies may be emphasized, while for distortion-sensitive components, melt pool geometry and thermal 109596161.1LLNL-077518-8097. WOOOhistory features that correlate with residual stress formation may be emphasized. The system may therefore be configured to output a tailored set of microstructure descriptors as “predictive microstructure” for a given component class, material, and printing strategy, while still operating within the same accelerated digital twin framework in which energy deposition is predicted by a surrogate and microstructure evolution is predicted by a second surrogate ora reduced-order model.

[0037] In various embodiments, the accelerated simulation techniques described herein are applicable to multiple additive manufacturing modalities in which an energy beam interacts with a workpiece and / or a powder bed to produce melting and resolidification, including laser powder bed fusion, laser directed energy deposition, and electron beam powder bed fusion. While laser-based systems commonly exhibit interface-dominated absorption and reflection behavior that motivates ray tracing of optical rays incident on evolving free surfaces, electron-beam systems typically exhibit a more volumetric energy deposition behavior in which charged particles penetrate into material and deposit energy over a depth distribution that depends on beam energy, material composition, density, and instantaneous thermal state. The systems and methods described herein provide a unified framework in which a high-fidelity energy deposition simulator is replaced or accelerated by a trained surrogate model, and in which the surrogate can be configured to model either interface-dominated deposition or volumetric deposition depending on the modality.

[0038] In laser-based embodiments, a ray tracing simulator may be executed to compute absorbed energy deposition as a function of incident rays, reflection events, and absorption at surfaces. The simulator may use as inputs a three-dimensional representation of geometry and material distribution, such as a metal volume fraction field on a voxel grid, and one or more fields representing the thermal state of the build, such as a temperature field. The simulator may output a three-dimensional absorbed energy deposition field that is spatially sparse and concentrated near an interface. In such embodiments, the surrogate model may be trained using a loss function that emphasizes errors at or near an interface by applying an interface mask derived from the metal volume fraction field and by enforcing global energy consistency so that the surrogate’s predicted absorbed energy equals the absorbed energy computed by the simulator for a given incident beam power and exposure. The surrogate may further be trained to preserve characteristic spatial patterns associated with multi-reflection and view-factor effects, such as enhanced absorption in cavities or near re-entrant features where multiple reflections increase local energy density.119596161.1

[0039] In electron-beam embodiments, the energy deposition process may be modeled as a volumetric distribution that extends beneath a top surface and may include scattering and attenuation phenomena. In these embodiments, the energy deposition simulator used to generate training data may include a charged-particle transport solver, an empirical penetration-depth model, or a physics-based model that approximates electron stopping power and volumetric absorption as a function of material density and beam parameters. The simulator may output a volumetric absorbed energy deposition field in which energy is deposited throughout a region of finite depth below a top surface, potentially with a depth-dependent profile and lateral spread that varies with beam energy, focus, and interaction volume. Because the deposition is not confined to a narrow surface layer, a surface-only interface mask is not required to capture the principal support of the deposition field, and training may instead weight a volumetric region of interest that encompasses the interaction volume. In some embodiments, the region of interest is defined by a combination of geometric and thermophysical criteria, such as a neighborhood around the beam centerline within a specified radius, a band of material beneath the top surface within a predicted penetration depth, and / or a region where temperature is within a specified range that indicates proximity to melting or softening. In these embodiments, the same general surrogate structure can be used, while the supervision strategy and loss weighting are adjusted to reflect volumetric deposition.

[0040] In certain embodiments, a surrogate model is configured to accept modality parameters that cause the same trained architecture class to operate in a laser mode or an electron-beam mode. Such modality parameters may include a modality indicator and one or more physical descriptors such as wavelength or polarization for laser systems, and beam energy or accelerating voltage for electron-beam systems. The surrogate may additionally receive material descriptors that affect absorption and penetration, such as density, reflectivity, and effective stopping power proxies. In some embodiments, these modality and material descriptors are encoded as additional input channels that are constant within a region for a given simulation instance, enabling the surrogate to learn conditional behaviors across modalities without requiring separate architectures.

[0041] In certain embodiments, training data generation for electron-beam systems is conducted in a manner analogous to the laser-based training data generation described herein, with the difference that the high-fidelity simulator used to produce target deposition fields is configured for charged-particle deposition. A plurality of simulation instances are generated that vary beam power, beam energy, scan speed, spot size, focus condition, and scan strategy, as well as material state and geometry. For each 129596161.1LLNL-077518-8097. WOOOinstance, one or more input fields are recorded that represent the evolving workpiece state, including a temperature field and a material distribution field, and one or more target fields are recorded that represent the volumetric absorbed energy deposition produced by the simulator. In some embodiments, the material distribution field includes a metal volume fraction field that represents powder packing density and solid material occupancy. Because powder beds can have density variations and because electron penetration depends on density, the metal volume fraction field can be used as a proxy for spatially varying absorption depth and lateral scatter. In certain embodiments, the surrogate learns a mapping from temperature and metal volume fraction to volumetric deposition that implicitly captures the effect of temperature-dependent density or phasedependent interaction behavior.

[0042] In some embodiments, preprocessing steps are applied to simulation outputs before training to ensure stable learning across modalities. In laser-based embodiments, preprocessing may include reconstructing an interface, smoothing or filtering to reduce ray sampling noise, and scaling deposition to satisfy energy balance constraints. In electron-beam embodiments, preprocessing may include normalizing deposition profiles to remove dependence on absolute beam power when training a shape predictor, separating the deposition into a normalized spatial distribution and a scalar absorbed energy value, and optionally applying smoothing consistent with the physical interaction volume. In certain embodiments, the surrogate is trained to predict a normalized volumetric deposition shape, and a separate scalar model predicts a total absorbed energy or coupling efficiency, and the final deposition field is obtained by multiplying the normalized shape by the absorbed energy scalar and enforcing nonnegativity and energy conservation.

[0043] In some embodiments, the surrogate is integrated into a thermal solver or a coupled multiphysics simulation pipeline. A thermal update step may compute the next temperature field given a predicted deposition field and heat transfer mechanisms including conduction, convection, and radiation. The surrogate may be invoked at each time step, at each beam position, or at a subset of time steps selected to balance accuracy and speed. In electron-beam embodiments, because the deposition is volumetric and may extend below the surface, the thermal update may incorporate deposition into volumetric elements rather than applying it as a surface heat flux. In laserbased embodiments, the deposition may be applied predominantly near the surface or within a shallow region defined by an effective optical penetration depth. In both cases, the model output is a three-dimensional deposition field that is compatible with the 139596161.1discretization of the thermal solver.

[0044] In certain embodiments, a worked example for an electron-beam powder bed fusion process is provided to illustrate the changes relative to laser-based embodiments. A build region is discretized on a voxel grid and initialized with a metal volume fraction field that represents powder packing and a temperature field representing preheat conditions. A high-fidelity charged-particle deposition simulator is executed for a plurality of beam positions and scan conditions to generate volumetric deposition fields for training. A three-dimensional convolutional neural network surrogate is trained to predict the volumetric deposition field given the temperature field, the metal volume fraction field, and one or more beam descriptors including beam energy and beam power. The loss function includes a volumetric reconstruction term over a region of interest that spans the interaction volume, together with a global energy constraint term that forces the integral of the predicted deposition field to match the absorbed energy of the simulator output for each instance. After training, the surrogate is deployed to replace the charged-particle simulator during thermal simulation, enabling evaluation of many candidate scan strategies. The predicted temperature histories are then used fordownstream predictions such as melt pool geometry and microstructure descriptors, and in some embodiments are used to evaluate the likelihood of defects or to guide modification of printer instructions.

[0045] In certain embodiments, the same general approach supports modalityspecific physics through changes to the definition of the region of interest, the formation of masking or weighting functions, and the inclusion of modality descriptors. For example, in laser-based embodiments, a weighting function may emphasize interface voxels because absorption occurs at the free surface and is strongly affected by geometry-driven multiple reflection, whereas in electron-beam embodiments the weighting function may emphasize voxels within a predicted penetration depth distribution and may optionally emphasize density gradients that influence scattering. In certain embodiments, the weighting function is learned as an auxiliary output of the surrogate, such as a predicted interaction-volume mask or attention map that identifies where deposition is expected to occur, and the reconstruction loss is applied preferentially where the attention map indicates deposition support. This learned interaction-volume mask can be used as a diagnostic output and can also enable adaptive refinement, in which higher spatial resolution is used only where the model predicts a concentrated deposition region.

[0046] In some embodiments, the surrogate model is used to generate deposition fields for different materials and powder conditions by conditioning on material 149596161.1descriptors and powder density descriptors. For example, in electron-beam embodiments, the surrogate may be conditioned on a density field derived from the metal volume fraction and on a beam energy descriptor, allowing the surrogate to learn that higher density materials and higher beam energies correspond to different penetration and scattering behavior. In laser-based embodiments, the surrogate may be conditioned on reflectivity or absorptivity descriptors and may learn how these parameters affect the spatial distribution of absorbed energy, including in cavities and near re-entrant features. In both modalities, the resulting deposition field prediction may be used for pre-print analysis, qualification, and optimization, including selecting scan parameters and scan sequences that produce desired thermal histories and microstructure outcomes while minimizing defect risk and build time.

[0047] In certain embodiments, the modality-general energy deposition surrogate is paired with downstream surrogates or reduced-order models that predict microstructure and / or distortion, enabling an end-to-end accelerated digital twin workflow. The deposition surrogate provides deposition fields rapidly enough to enable repeated simulation of many candidate printer instructions. The downstream predictor consumes temperature histories and / or derived thermal features, together with geometric and boundary-condition descriptors, to produce microstructure descriptors and / or distortion metrics. In this manner, a single framework supports multiple energy-beam modalities by altering the training data generation mechanism for deposition, adjusting loss weighting to reflect interface versus volumetric deposition, and optionally including modality-specific descriptors, while keeping the overall pipeline and software integration substantially the same.

[0048] In certain embodiments, training data for the accelerated energy-deposition prediction models described herein is generated using a high-fidelity digital twin that couples a multiphysics solver with a laser ray tracing solver. The multiphysics solver may compute transient thermal fields and phase or material state fields in response to an applied heat source, and the laser ray tracing solver may compute an absorbed energy deposition field that accounts for geometric optics effects, including reflection and absorption at interfaces, multiple reflections in cavities or re-entrant regions, and occlusion or shadowing due to local topography. In some embodiments, the ray tracing solver is executed at a sequence of beam positions corresponding to printer instructions, and the resulting absorbed energy deposition field is stored as a ground-truth target for training a surrogate model.

[0049] In various embodiments, the training dataset is constructed to promote 159596161.1generalization across both geometrical complexity and process conditions, including to geometries and toolpaths not explicitly represented in the training set. In some embodiments, training data generation begins with a set of canonical or “simple” geometries chosen to span fundamental interface and cavity configurations that drive ray tracing outcomes. Such canonical geometries may include, without limitation, planar surfaces with varying inclination, single tracks, overlapping tracks, grooves, ridges, steps, holes, pockets, channels, thin walls, overhangs, lattice-like features, and re-entrant geometries. In certain embodiments, these canonical geometries are parameterized so that a family of instances can be generated by varying geometric parameters such as feature depth, feature width, wall thickness, tilt angle, corner radius, and cavity aspect ratio. By sampling parameterized families, the training set includes a large diversity of local interface configurations while retaining computational tractability in the high-fidelity simulations used to produce ground-truth deposition.

[0050] In some embodiments, the training dataset is additionally stratified over surface condition regimes that affect reflection and absorption. Surface condition may be represented explicitly, such as by a roughness field defined on an interface, or may be represented implicitly by geometric micro-topography embodied in a metal volume fraction field or a reconstructed interface. In certain embodiments, roughness regimes are sampled by generating realizations of surface topography with different statistical parameters, such as mean roughness and correlation length, or by generating powderbed surface conditions with varying packing density and particle size distributions. In these embodiments, the ray tracing solver is executed on each realization, thereby generating deposition fields that reflect how multi-reflection and local incidence angles change with roughness. The surrogate model is trained on examples spanning multiple roughness regimes so that it learns deposition behaviors that are robust to realistic interface variability.

[0051] In some embodiments, the training dataset is also stratified over powder packing states and material distribution states. Powder packing state may be represented by a metal volume fraction field that varies spatially and captures powder density, partially melted regions, and the evolving boundary between consolidated material and unconsolidated powder. In certain embodiments, multiple powder packing realizations are generated for the same nominal geometry and scan condition, thereby producing training pairs that isolate the effect of packing variability on energy coupling and absorbed deposition. In some embodiments, powder packing state is varied in concert with scan parameters to represent regimes in which the powder bed is largely unchanged by the 169596161.1beam, regimes in which partial consolidation occurs, and regimes in which repeated scanning or remelting modifies surface morphology.

[0052] In some embodiments, the training dataset spans a plurality of process regimes that materially influence deposition and thermal response, including regimes associated with conduction-mode melting, transition-mode behavior, and keyhole-mode behavior. In these embodiments, the dataset includes training instances at different combinations of laser power, scan speed, hatch spacing, and spot size such that the resulting thermal fields and interface shapes correspond to different melt pool geometries and different degrees of surface depression or cavity formation. Because ray tracing outcomes are sensitive to re-entrant cavities and steep surface angles, inclusion of keyhole-like geometries or other cavity-forming regimes in the training set can improve generalization to process windows where multiple reflections significantly increase coupling. In some embodiments, the dataset is balanced so that the surrogate does not overfit to a single regime, and the sampling distribution is configured to include both common operating conditions and edge cases that would otherwise be underrepresented.

[0053] In certain embodiments, the training dataset includes variation in scan strategy and toolpath context. Toolpath context may include, without limitation, scan direction relative to geometry, scan rotation between layers, contour strategies, and the proximity of the beam path to previously scanned tracks. In some embodiments, training instances include isolated single-track scans, hatch scans with varying overlap, and contour-plus-hatch sequences. In some embodiments, the ray tracing target is computed for beam positions that include both steady-state scanning segments and transient segments such as turnarounds, starts, and stops, thereby exposing the surrogate to deposition patterns associated with rapid changes in local geometry and thermal state.

[0054] In some embodiments, the dataset is constructed using a two-stage sampling strategy. In a first stage, a broad distribution of simulation instances is generated on canonical geometries and parameterized families to cover a wide space of interface configurations and process parameters. In a second stage, additional simulation instances are generated adaptively based on model error, uncertainty, or coverage metrics. For example, after an initial surrogate is trained, the surrogate may be evaluated on a set of candidate geometries or scan strategies that are outside the canonical families, such as complex lattice structures, part-scale features, or assemblies with supports. Regions or conditions in which the surrogate exhibits elevated error relative to ray tracing, or elevated predictive uncertainty, are identified and used to select new high- 179596161.1fidelity simulations for inclusion in the training set. In this manner, the training set can be expanded efficiently to address domain shift without requiring exhaustive simulation across all possible geometries.

[0055] In certain embodiments, training examples are formed by extracting local three-dimensional windows or patches centered on beam positions or locations of interest. The patch may include fields such as metal volume fraction and temperature, and may include derived fields such as an interface indicator and thermal gradients. Patches can be extracted from larger simulation domains so that the surrogate learns local deposition physics that generalize across parts, while reducing the computational cost and memory requirements of training. In some embodiments, patch extraction is performed with overlap and at multiple orientations, and augmentation is applied by rotating or reflecting patches to exploit symmetries in the physics, thereby increasing effective dataset diversity and improving invariance to scan direction.

[0056] In certain embodiments, the dataset includes held-out geometries and held-out process windows for validation and for establishing generalization. Held-out geometries may include complex geometries not used for training, such as lattice structures, parts with internal channels, or geometries with multiple interacting features, and held-out process windows may include parameter sets not used fortraining, such as combinations of power and speed near a boundary between melting regimes. In some embodiments, validation includes comparing the surrogate's predicted absorbed energy deposition field to the ray tracing target using one or more metrics including per-voxel absolute error, error concentrated near interfaces, and error in global absorbed energy. In some embodiments, validation further includes downstream performance validation in which the surrogate’s predicted deposition is used within the multiphysics solver to compute temperature evolution, melt pool geometry, and other derived quantities, and these derived quantities are compared against corresponding quantities obtained when the ray tracing solver is used. Because small deposition differences can compound over time, downstream validation provides evidence that the surrogate is sufficiently accurate for integration into a time-stepping simulation pipeline.

[0057] In certain embodiments, the system is configured to quantify uncertainty associated with surrogate predictions and to use that uncertainty to maintain reliability in deployment. In some embodiments, uncertainty is estimated using an ensemble of surrogate models, Bayesian approximations such as dropout-based inference, or learned heteroscedastic variance outputs. In some embodiments, the system computes an uncertainty field aligned with the predicted deposition field, indicating spatial regions 189596161.1where predicted deposition is less certain. In some embodiments, uncertainty is summarized as a scalar confidence score for a beam position or patch. In certain embodiments, the system compares the confidence score to one or more thresholds and determines whether to accept the surrogate prediction or to invoke a higher-fidelity solver.

[0058] In some embodiments, a fail-safe logic is implemented that selectively falls back to ray tracing when the surrogate is likely to be outside its domain of validity. In some embodiments, fallback triggers include, without limitation, predictive uncertainty above a threshold, detection of geometrical configurations associated with multiple reflections not adequately represented in training, detection of thermal states associated with regime transitions, and detection of extreme interface slopes or re-entrant features that create narrow cavities. In certain embodiments, when fallback is triggered, the ray tracing solver is executed only for the affected beam positions or patches, and the resulting high-fidelity deposition is inserted into the simulation pipeline while the surrogate continues to be used elsewhere. In some embodiments, the high-fidelity results obtained during fallback operation are stored and may be used to further train or fine-tune the surrogate model, thereby implementing an active learning loop that improves coverage overtime.

[0059] In certain embodiments, the system is configured to fuse surrogate predictions and ray tracing results. For example, when fallback is triggered for only a subset of a patch or a subset of beam positions, the system may combine deposition fields by blending, by replacement in regions of high uncertainty, or by enforcing conservation constraints on a composite deposition field. In some embodiments, fusion is performed such that global absorbed energy remains consistent with the beam power and coupling assumptions, and such that discontinuities at boundaries between surrogate-predicted regions and ray-traced regions are minimized through smoothing or conservative remapping.

[0060] In some embodiments, the dataset generation and validation strategy described herein enables training on computationally manageable simulation instances, such as canonical geometries and reduced build domains, while still achieving accurate prediction on complex part geometries and full-build contexts. By explicitly sampling across geometry classes, roughness regimes, powder packing states, melting regimes, and scan strategies, and by validating on held-out geometries and held-out parameter windows, the surrogate model can be trained to generalize beyond the training distribution. By further incorporating uncertainty quantification and selective fallback to high-fidelity ray tracing, the deployed system maintains robustness in cases of domain 199596161.1shift, thereby enabling accelerated simulation that is both fast and reliable for process planning, qualification, and printer instruction modification workflows.

[0061] In certain embodiments, training data for the neural-network surrogate is produced by coupling a high-fidelity multiphysics solver with a laser ray tracing solver such that both solvers exchange fields on a regular three-dimensional grid. In one nonlimiting implementation, a hydrodynamic thermal-fluid solver is coupled to a laser ray tracing module such that the laser module receives, on a uniform grid, a materialdistribution field (e.g., metal material fraction or volume fraction) and a temperature field, and returns, on the same grid, an absorbed laser energy deposition field. The coupling may be executed at each timestep, or at a subset of timesteps, with time variation arising as an emergent property of the closed-loop interaction between the deposited laser energy and the hydrodynamic time stepping. In this manner, the training corpus inherently encodes the non-linear feedback between deposition, temperature, melt pool geometry, and interface evolution that gives rise to conditions such as re-entrant depressions and multiple reflections.

[0062] In various embodiments, the surrogate is configured as a three-dimensional fully convolutional network that accepts as input a three-dimensional tensor comprising at least two channels: a first channel containing the material distribution (e.g., volume fraction) and a second channel containing temperature, and outputs a three-dimensional tensor with a single channel representing absorbed energy deposition per grid cell. In certain embodiments, a binary interface mask is generated from the material distribution to identify metal-gas interface voxels, and the mask is used to restrict training loss calculation to the interface and to enforce physically valid inference behavior by discarding predictions in air or bulk interior regions where energy deposition cannot occur. In some embodiments, the mask is not provided to the network as an input channel; instead, the mask is used during loss computation and during inference postprocessing, such that the model learns a mapping from the physically meaningful inputs without being explicitly conditioned on the mask, while still ensuring that only admissible outputs are utilized.

[0063] In some embodiments, the training loss includes an interface-local term that penalizes voxelwise error on the interface and a global constraint term that enforces conservation of absorbed energy on the interface. One example loss includes a mean L1 error over interface voxels, normalized by the interface area to avoid over-weighting timesteps with larger surface area, together with an absolute difference between total predicted absorbed energy and total ground-truth absorbed energy summed over the 209596161.1interface voxels. In certain embodiments, this conservation term is treated as a numerical-stability requirement for inline deployment, because cumulative absorbed energy drives the global temperature evolution and violations can lead to unphysical behavior or instability in the coupled multiphysics simulation. In some embodiments, training further includes data normalization such that input channels are scaled to have approximately unit standard deviation to improve optimizer conditioning.

[0064] In certain embodiments, the surrogate architecture is a memory-efficient “squeeze ll-net” that combines an encoder-decoder topology and skip connections with parameter-efficient convolutional modules so that the network can reside in memory alongside a large multiphysics code. In some embodiments, the architecture downsamples spatial extents by a factor of two per layer (e.g., via 2x2x2 max pooling) until the representation is compressed to approximately a 3x3x3 grid or smaller, thereby allowing global geometric context to influence local deposition predictions through the contraction-expansion pathway while remaining computationally tractable. In some embodiments, channel growth is moderated relative to standard U-net designs to reduce memory footprint, for example by increasing channels by approximately \2 per layer rather than doubling at each layer, while still permitting a sufficiently wide network to represent non-local reflection and shadowing effects. In some embodiments, the resulting network has on the order of 71k parameters, enabling fully in-memory deployment on modern compute nodes and avoiding large memory bandwidth overheads.

[0065] In some embodiments, training targets are post-processed prior to learning to reduce discretization artifacts while preserving physically meaningful features such as shadows. For example, because only a finite number of rays may be sampled per timestep (e g., 1500 rays) and ray strike locations introduce sampling noise into the raw deposition field, the raw deposition may be smoothed (for instance, by a weighted average between face-adjacent voxels) and then rescaled so that the total absorbed energy matches the absorbed energy budget at that timestep; the smoothed-and-rescaled deposition field may be used as the ground truth for learning. In some embodiments, simulation outputs from adaptive unstructured grids are interpolated onto uniform grids suitable for deep learning tensor inputs, and interface reconstruction is performed during transfer to preserve mass conservation and boundary continuity.

[0066] In various embodiments, the surrogate is deployed in-the-loop with the multiphysics solver as a drop-in replacement for the ray tracing call at each laser position update, each solver cycle, or each timestep, depending on the temporal resolution used 219596161.1LLNL-077518-8097. WG00by the simulation. In one mode of operation, the multiphysics solver advances a timestep by (i) computing or updating the material distribution and temperature fields, (ii) interpolating these fields onto the uniform grid used by the surrogate (when the solver’s internal discretization differs), (iii) invoking the surrogate to predict the absorbed deposition field, (iv) applying the binary interface mask to the surrogate output to enforce physical admissibility, and (v) using the masked deposition field as a source term for the subsequent thermal-fluid update. In some embodiments, the surrogate inference is performed on CPU “in place” on a single socket to minimize data movement and to simplify integration with legacy HPC codes, and in other embodiments inference is performed on GPU to exploit substantially lower inference latency. In one non-limiting performance comparison, a baseline ray tracing invocation in a relatively flat-surface laser powder bed fusion test case required approximately 1323 milliseconds per invocation when run in parallel on 560 processes, while the surrogate required approximately 340 milliseconds on a single socket of the same system, yielding a worstcase wall-clock speedup of about 4x; on more complex geometries where ray tracing steps may take as long as about 13000 milliseconds, the surrogate’s essentially geometry-independent inference time yields speedups of up to about 40x, and GPU inference times on a V100 GPU are reported on the order of 23 milliseconds.

[0067] In some embodiments, the deployment loop further includes caching and reuse mechanisms to reduce overhead in parameter sweeps, multi-track interactions, and repeated evaluations of candidate toolpaths. For example, because the surrogate inference cost is stable and does not depend on the number of rays or the complexity of reflections, the system can evaluate candidate scan strategies by repeatedly invoking the surrogate across many beam positions and timesteps while holding other physics modules constant. In certain embodiments, the system caches intermediate representations derived from the input fields, such as the interface mask, local interface normals, or other derived geometric descriptors computed by the multiphysics solver for unrelated physics packages, and reuses these derived representations to avoid recomputation when only the beam position changes. This reduces the marginal cost per surrogate invocation and improves overall throughput for multi-track and multi-layer simulations that are otherwise impractical when full ray tracing dominates wall time.

[0068] In some embodiments, a selective fallback mechanism is provided to preserve reliability under domain shift while maintaining acceleration. For example, the system may compute a confidence measure associated with a given surrogate inference, such as a discrepancy between predicted absorbed energy and an expected absorbed- 229596161.1energy budget implied by beam power, or a heuristic indicator of geometric novelty such as extreme concavity or rapid interface topology changes. When the confidence measure indicates elevated risk, the system can invoke the full ray tracing module forthat timestep or region while continuing to use the surrogate elsewhere, and optionally store the resulting high-fidelity deposition field for subsequent retraining or fine-tuning. This approach is consistent with the principle that energy conservation and admissible deposition support are critical for stable in-loop operation, and that the surrogate can be integrated inline with a multiphysics code to unlock parameter exploration and larger domains without sacrificing the fidelity required for digital twin simulations.

[0069] In some embodiments, the disclosed accelerated digital twin workflow further includes a reduced-order modeling pathway configured to predict distortion, warpage, or other dimensional deviation of a workpiece attributable to residual stress and thermo-mechanical response, and to use such predictions to modify printer instructions. This insertion is intended to supplement the Detailed Description of the revised nonprovisional draft.

[0070] In certain embodiments, a high-fidelity thermo-mechanical simulation is used to generate training data for distortion prediction. The thermo-mechanical simulation may be executed using a finite element solver or multiphysics solver configured to model thermal loading from an additive manufacturing process and the resulting mechanical response, including elastic and plastic strain, residual stress accumulation, and displacement of the workpiece relative to a nominal geometry. The thermo-mechanical simulation may receive as inputs one or more of a time history of temperature, a time history of thermal gradients, material properties including temperature-dependent elastic modulus, yield stress, and thermal expansion coefficient, boundary conditions including fixture constraints and contact conditions, and process descriptors derived from printer instructions such as scan order, scan vectors, interlayer dwell, and hatch spacing. In some embodiments, the thermo-mechanical simulation is executed on the full part geometry; in other embodiments, it is executed on a subdomain, a representative volume, or a reduced model that preserves the dominant distortion modes for a class of geometries. In some embodiments, the thermo-mechanical simulation is executed fora plurality of printer instruction variants and parameter settings to generate a training corpus spanning process windows, scan strategies, and part / support configurations.

[0071] In certain embodiments, the training outputs for distortion include one or more displacement fields defined over a mesh, including a three-component 239596161.1displacement vector field u(x) = (ux, uy, uz) at nodes or elements, and / or one or more derived scalar distortion metrics. Examples of derived metrics include out-of-plane deflection of a surface, maximum nodal displacement, peak-to-valley deviation of a specified surface relative to a CAD surface, deviation at specified datum features, twist angle, bow magnitude, and global alignment error after best-fit rigid registration. In some embodiments, outputs further include residual stress tensors, plastic strain fields, or curvature fields, and these fields may be used as auxiliary labels during training to improve generalization or to enable multi-task learning.

[0072] In some embodiments, distortion prediction is performed using a graphbased reduced-order representation in which the workpiece geometry and / or simulation discretization is encoded as a graph. A graph may be constructed from a finite element mesh by defining nodes corresponding to mesh nodes, element centroids, or surface nodes, and defining edges that represent adjacency or proximity relationships. In one example, an undirected edge is created between two nodes if they share an element, share a face, share an edge, or are within a distance threshold in Euclidean space. In some embodiments, edge features are included to encode geometric relationships, such as edge length, relative position vector, surface normal differences, or local thickness. In some embodiments, node features include spatial coordinates, material identifiers, boundary condition flags, support / contact flags, and one or more process-derived fields mapped onto the mesh such as temperature, thermal gradient magnitude, cooling rate proxy, or cumulative absorbed energy proxy. In some embodiments, node features further include history features such as maximum temperature experienced at the node, time above a threshold temperature, ora summary of layer-wise thermal exposure.

[0073] In some embodiments, the distortion pathway receives as its primary inputs one or more fields produced by the accelerated thermal simulation described elsewhere in the application, including temperature and / or a derived thermal history, and produces as its primary outputs one or more distortion metrics and / or a predicted displacement field. In these embodiments, the distortion pathway operates as a downstream model coupled to the energy-deposition surrogate and thermal time stepping. In some embodiments, the distortion pathway is trained and deployed separately from the energydeposition surrogate, such that the distortion model can accept either (i) thermal histories generated using the surrogate-accelerated thermal simulation or (ii) thermal histories generated using a different simulator, provided that the inputs are normalized and mapped to the graph representation in a consistent manner.

[0074] In certain embodiments, the distortion reduced-order pathway comprises a 249596161.1LLNL-077518-8097. WOOOgraph convolutional autoencoder configured to encode high-dimensional distortionrelevant fields into a low-dimensional latent representation. In some embodiments, the encoder receives node features that include at least one of displacement vectors, residual stress components, plastic strain, or thermal history features, and outputs a latent embedding vector z for each node and / or a global latent vector zglobal for the entire part. In some embodiments, zglobal is obtained by pooling node embeddings using mean pooling, sum pooling, attention pooling, or hierarchical pooling based on mesh partitions. In some embodiments, the decoder of the autoencoder is configured to reconstruct one or more target fields, such as the displacement field u(x) at nodes, from the latent representation. In these embodiments, the autoencoder is trained to minimize a reconstruction loss that penalizes discrepancies between reconstructed fields and ground-truth fields from the thermo-mechanical simulations, optionally with weighting on surface nodes or functional features to reflect that distortion at interfaces and datum features is of particular practical relevance.

[0075] In some embodiments, the graph convolutional autoencoder is configured to capture non-local coupling that drives distortion, such as the fact that constraint conditions and thermal gradients in one region can induce displacement and curvature in distant regions through structural connectivity. In some embodiments, message passing layers propagate information across edges and update node embeddings using learned aggregation functions, thereby allowing the encoder to form latent representations that reflect global stiffness paths and constraint propagation while still operating on irregular meshes. In some embodiments, the autoencoder includes residual connections, normalization layers, and non-linearities to improve stability, and is trained with regularization to encourage smooth latent representations that correspond to physically plausible deformation modes.

[0076] In certain embodiments, the latent representation is used as an intermediate reduced-order state that enables fast regression from process descriptors to distortion outcomes. In some embodiments, a regression model is trained to map from (i) a vector of process parameters and / or scan-strategy descriptors and / or lowdimensional thermal summary features to (ii) a latent representation produced by the autoencoder encoder, and the predicted latent representation is then decoded to obtain a predicted displacement field or distortion metric. In some embodiments, the regression model comprises Gaussian process regression, which in addition to predicting a mean value for the latent variables or distortion metrics also provides an uncertainty estimate such as a predictive variance. In these embodiments, the Gaussian process regression 259596161.1may be trained on pairs (p, z) where p denotes a vector of process descriptors and z denotes the latent representation obtained by encoding a field from a high-fidelity thermomechanical simulation. In some embodiments, the regression targets comprise a subset of latent dimensions selected to represent dominant distortion modes, and remaining latent dimensions are discarded or regularized to reduce noise.

[0077] In some embodiments, the regression model predicts distortion metrics directly rather than predicting latent variables. In such embodiments, Gaussian process regression or another regression model is trained on pairs (p, d) where d comprises one or more scalar distortion metrics such as maximum displacement or surface deviation at a specified region of interest. In other embodiments, the regression model predicts latent variables, and the decoder reconstructs a full displacement field, enabling downstream evaluation of arbitrary geometric tolerances and feature-based deviation criteria without retraining the regression model for each metric.

[0078] In certain embodiments, training data for the distortion pathway is generated using a coordinated sampling strategy that varies printer instructions and process parameters to populate a space of likely distortion responses. In some embodiments, the sampling includes variations in scan order, scan direction rotation between layers, contour / hatch scheduling, support placement or density, and baseplate constraint conditions. In some embodiments, the sampling includes variations in energy input parameters such as beam power and scan speed that affect thermal gradients and thus residual stress, and variations in dwell and preheat that affect stress relaxation. In some embodiments, the sampling includes variations in part orientation and build layout on the build plate, which affect constraint and heat dissipation paths. In some embodiments, the sampling strategy includes adaptive enrichment in regions where preliminary distortion models show high error or high uncertainty, thereby improving coverage of regime boundaries such as the transition from predominantly elastic springback to significant plastic deformation.

[0079] In some embodiments, the distortion pathway includes a mapping step that converts outputs of the thermal simulation into node features on the distortion graph. For example, a temperature history on a voxel grid may be interpolated onto mesh nodes of the thermo-mechanical model, and summary features such as peak temperature and cooling rate proxy may be computed per node and appended as node features. In some embodiments, the thermal history features are computed layer-wise and then aggregated into a smaller set of descriptors that preserve dependence on scan sequencing, such as a vector of per-layer peak temperatures or per-layer integrated absorbed energy. In some 269596161.1embodiments, the mapping step is configured to preserve locality near thin walls, overhangs, and support interfaces, where distortion is particularly sensitive to constraint release and thermal gradients.

[0080] In certain embodiments, the distortion pathway outputs are used to modify printer instructions. In one mode of operation, a set of candidate printer instructions is evaluated by running the surrogate-accelerated energy-deposition and thermal simulation to obtain thermal histories, and then applying the distortion pathway to predict a distortion metric and an associated uncertainty estimate. Candidate instructions that produce distortion metrics exceeding a threshold or that have high uncertainty may be rejected, and candidates that satisfy dimensional criteria with sufficient confidence may be selected. In another mode of operation, the system performs an optimization in which one or more printer instruction parameters are adjusted to minimize a predicted distortion objective, optionally subject to constraints on build time, microstructure targets, or defect risk proxies. In some embodiments, the predicted distortion objective includes a weighted combination of multiple metrics, such as maximum out-of-plane deflection plus deviation at datum features, and the weights may be selected based on tolerance requirements for the part.

[0081] In some embodiments, the optimization uses the uncertainty output of Gaussian process regression to guide exploration. For example, the system may use an acquisition function that balances predicted distortion reduction against uncertainty to select new candidate printer instruction settings for evaluation, thereby accelerating convergence to low-distortion settings with fewer high-fidelity thermo-mechanical simulations. In some embodiments, when uncertainty exceeds a threshold, the system triggers execution of a high-fidelity thermo-mechanical simulation for the corresponding candidate, and adds the result to the training set to update the regression model and / or the autoencoder, thereby implementing an active-learning loop for distortion prediction.

[0082] In some embodiments, the distortion pathway supports compensation of printer instructions by generating a geometry compensation field. In one non-limiting example, the predicted displacement field is used to compute an inverse compensation vector field that is applied to a nominal geometry or to toolpath coordinates so that the as-printed part is closer to nominal after distortion occurs. In some embodiments, the compensation is applied globally as a pre-deformation of the build geometry; in other embodiments, it is applied locally to selected features or surfaces. In some embodiments, the compensation is constrained to maintain manufacturability, such as limiting local curvature or ensuring that compensated toolpaths remain within machine travel limits and 279596161.1maintain valid scan overlaps.

[0083] In certain embodiments, the distortion pathway is integrated with the microstructure prediction pathway such that tradeoffs between microstructure objectives and distortion objectives are evaluated jointly. In one example, the system generates candidate scan strategies, predicts absorbed energy deposition and thermal histories, predicts microstructure descriptors indicating grain structure or defect risk, and predicts distortion metrics indicating dimensional deviation, and selects or modifies printer instructions based on a multi-objective criterion. In some embodiments, this criterion prioritizes achieving a microstructure target while constraining predicted distortion below a tolerance band; in other embodiments, it prioritizes dimensional accuracy while ensuring that micro structure descriptors remain within acceptable ranges.

[0084] In some embodiments, the distortion reduced-order pathway is configured to produce outputs at different granularities depending on computational budget and decision needs. For rapid screening, the regression model may output one or more scalar distortion metrics and uncertainties. For detailed evaluation, the regression may output latent variables that are decoded to reconstruct a full displacement field, enabling computation of deviations on arbitrary surfaces and features. In some embodiments, the decoded displacement field is used to compute a predicted deformed geometry, and the predicted deformed geometry is compared to the nominal geometry to generate a deviation map that can be used in tolerance analysis and to guide design of supports or scan strategies.

[0085] In certain embodiments, the distortion pathway is implemented such that it can operate on different part geometries by constructing graphs from corresponding meshes and by encoding geometric and boundary-condition descriptors as node and edge features. In some embodiments, to improve generalization across part geometries, the autoencoder and regression models are trained on a dataset comprising multiple geometries and support configurations, and include normalization and pooling operations that permit variable node counts. In some embodiments, the models are fine-tuned for a specific part family using a small number of high-fidelity thermo-mechanical simulations, thereby enabling deployment for production-relevant geometries with limited additional simulation cost.

[0086] FIG. 1 is a block diagram of a neural network system 100 in accordance with some example embodiments. The neural network system 100 includes a neural network architecture 102 which receives training data 104 from a laser ray tracing simulator 106. In some embodiments, the neural network architecture 102 includes two 289596161.1models 108, 110 topologically arranged to feed output of the first as a portion of input into the second. In some embodiments, the first network 108 is a computer vision model and the second model 110 is a mesh-based simulation model. User input 112 is supplied to the neural network architecture 102 via post training usage.

[0087] User input includes predetermine input criterion 114. The input criteria are identified through feature engineering. Given that the disclosed method and system makes use of simulation data, identifying the process factors that are dispositive of end workpiece results is a difficult challenge. A complex simulator can control any variable, but not every one of those variables is meaningful for training data or for input specifications. In some embodiments, the computer vision model includes:

[0088] (1) The volume fraction- when applied to laser energy deposits a value of 0 or 1 in a mesh zone meant pure gas or metal. A value in between meant an interface that the rays reflect off as light reflects off a mirror. In a scenario of laser energy deposits, the volume fraction applies to the materials or the gas. This factor operates differently in electron beam AM which deposits energy volumetrically. While the laser deposits on the surface, the electron beam energy can penetrate and deposit energy well below the surface. The volume fraction temperature applies to the volume of energy deposition as opposed to just the material / gas environment interface.

[0089] (2) Temperature distribution - which determines an amount of energy a laser ray will deposit over an interface zone.

[0090] (3) Output feature - laser energy deposition field that results from full laser ray tracing. In electron beam AM, the same feature engineering will apply inside the workpiece as well (applying to a volume as opposed to just a surface).

[0091] (4) Modifying the NN loss function to maintain conservation of energy.

[0092] In some embodiments, the mesh-based model includes as input features input features used:

[0093] (1) cellular automata state of a mesh zone. For example, whether a state of the mesh zone is liquid, solid, mushy or inactive.

[0094] (2) temperature of a given mesh zone.

[0095] (3) cooling rate of the melt pools.

[0096] (4) the thermal gradient of the melt pools.

[0097] (5) Octahedron lifetime in mesh zones.

[0098] (6) Octahedron orientation of mesh zones. For example, the dot product of thermal gradient and size orientation directions.

[0099] (7) grain ID - here the prediction identifies when liquid zones are captured 299596161.1LLNL-077518-8097. WG00during solidification the grain to which they belong. The state of a zone progresses from liquid to mushy to solid as time elapses during solidification. The state of a zone in a mesh determines if a liquid zone solidified and if so, to what solid microstructure or grain would it belong. Since each grain has its own crystallographic orientation, and each grain has its own grain ID, one can determine to what grain (ID) did the zone in question get captured into.

[0100] The input criteria are employed both in the user query and in the training data. The training data employs a number of variations on the input criterion. A given model may be trained based entirely on expected selections of the input criterion, such as through limited modifications of available printer materials and available 3D printer apparatuses. Architecture of the neural network employs either a single model with many or all trained variations, a plurality of many smaller models tuned for particular input criterion, ora combination thereof.

[0101] In addition to the input criterion describing the process variables, the user also has printer instructions 116 for AM to generate a physical workpiece (presumably, though not necessarily, with a complex geometry they wish to investigate and test). In response to input at the first network 108, the first network 108 generates a laser energy deposition field that simulates physics at an interface zone of the AM printer. That laser energy deposition field is supplied to the second network 110 which un turn extrapolates that laser energy deposition field across the extent of the AM printer instructions 116 resulting in a workpiece mi era structure 120.

[0102] FIG. 2 is a diagram of an AM printer 200 in accordance with some example embodiments. The AM printer 200 is used to form a three-dimensional shaped object on a table 202 to be described later by rapid prototyping, as well as to perform additive manufacturing by three-dimensional shaping on a workpiece (e.g. an existing component) W. Various embodiments of the AM printer 200 fall into a number of energy beam technologies. Examples include DED, laser powder bed fusion, electron beam AM, and laser welding.

[0103] Various embodiments of the AM printer 200 are equipped with; a movement system 204, a measurement system 206, and a computer system 600 including these systems that has overall control of the printer 200. In the description below, the lateral direction of the page surface in FIG. 2 will be described as a Y-axis direction, a direction orthogonal to the page surface will be described as the X-axis direction, a direction orthogonal to the X-axis and the Y-axis will be described as a Z-axis direction, and rotation (tilt) directions around the X-axis, the Y-axis, and the Z-axis will be described as 309596161.10x, 0y, and 0z directions, respectively.

[0104] Movement system 204 changes position of an interface zone (in this case, a surface on workpiece W on which a target portion is set). Movement is additionally induced by the positioning of a material feed 208 and a laser 210. Specifically, by driving the workpiece having the interface zone and the table 12 where the workpiece is mounted in directions of six degrees of freedom (6-DOF) (in each of the X-axis, the Y-axis, the Z-axis, the 0x, the 0y, and the 0z directions), position in directions of 6-DOF of the interface zone is changed.

[0105] Print instructions guide emission of print material 208 (e.g., powder or cable) and application of the laser 210 as well as the positioning of the interface zone. Changes to the print instructions ultimately modify the resultant workpiece W.

[0106] FIG. 3 is a flow diagram illustrating training a neural network in accordance with some embodiments. In step 302, a high-fidelity simulation data is generated by laser ray tracing simulators. The laser ray tracing simulations of microscale interactions of material melting and solidification that populate the neural network nodes simulate operation on simple workpiece geometries (e.g., cubes, pucks, or other minimally designed objects). Ultimately, the AM printer instructions are associated with more complex workpiece geometries (e.g., a full range of physical structures). Training data was generated using high-fidelity simulations of LPBF and DED. These are two of the most popular technologies in AM and most representative of laser melting problems. AN example case of the DED problem makes use of Ti-6AI-4V powder particles being deposited onto a convex melt pool surface irradiated by the laser. The example scenario creates a surface roughness that varies locally and as a function of time. In the LPBF problem, the surface starts flat and turns convex with time. Capturing the coupling of the laser energy deposition to the melt pool dynamics accurately is a crucial test of a U-net model (e.g., an image segmentation CNN model), as the varying surface temperature distribution resulting from the laser heating, creates a convex deep and narrow melt pool depression called a keyhole that achieves periodic oscillations, whereby the keyhole’s bottom oscillates vertically at ~40 Khz. In the above scenario and other embodiments sufficient training data is available via ALE3D, a multi-physics Arbitrary Lagrangian Eulerian hydrodynamic fluid dynamic code that is capable of incorporating different physics packages. In test to develop the teachings herein, ALE3D was coupled to the Livermore Laser Ray Tracing package (LLRT) to simulate laser beams striking, reflecting, and heating the metal surface.

[0107] Data exchange between the laser package and ALE3D occurs on a regular 319596161.13D grid, making this problem amenable to computer vision techniques. LLRT receives the metal material fraction and temperature on a 3D grid, and outputs a grid of laser energy deposited. Physically, the instantaneous energy deposited is a function of surface geometry, temperatures, and various laser parameters. Any time varying phenomena are an emergent property of how deposited laser energy impacts the hydrodynamic fluid time stepping.

[0108] Some embodiments further employ the CAFE algorithm for generation of training data. The CAFE algorithm (also referred to as CA) aims at predicting the time evolution of all solidifying grain structure. It is based on the Cellular algorithm (von Neumann, J. The general and logical theory of automata. In Taub, A. H. (ed.), Collected works — Design of computers, theory of automata and numerical analysis, volume V, pp.288-328. Pergamom Press, 1963.). Jon Von Neumann introduced CA in the context of self-reproduction of biological cells, but the method caught popularity because of its ability to generalize to complex evolutionary systems. Within CA, these are represented as cells defined usually on a uniform spatial grid. The state of each cell then changes as a function of time, given transition rules that involve the neighboring cells.

[0109] CAFE transition rules operate on a 2D uniform grid and with some modification to the growth and capture algorithm to 3D. Some embodiments make use of the 3D CAFE algorithm because it is more realistic but expensive. Each 3D CA cell can take on 4 CA states: liquid, solid, mushy (state in between solid and liquid at the solid / liquid interface) and non-CA material such as the gas above the metal alloy that obviously does not solidify. A temperature field is defined over that grid and is computed by coupling the thermal diffusion partial differential equation with the hydrodynamics that obeys Navie^s Stokes equations.

[0110] The heat source is a moving laser that heats the metal, liquefies it and as it moves away, the liquid cools down due to convective, radiative, evaporative and diffusive cooling and turns solid. An order parameter can be defined over each CA zone and is called the thermal under- cooling ATcell = Tliquidus_Tcell, or how colder is that zone relative to the liquidus temperature (temperature above which the material is completely liquid). When the liquid starts to transform into solid ATcell > 0 the most expensive part of the CA rules are active.

[0111] Several aspects of the CAFE algorithm make modeling expensive and complex for the graph neural network (GNN) to learn. First, the thermal hydrodynamics is solved on a separate grid. Time is spent transferring data to the CA grid. Furthermore, those zones that are actively solidifying, host a fictitious octahedron shape that either 329596161.1LLNL-077518-8097. WG00grows or shrinks in size, respectively indicating solidification or melting. This octahedron size evolution is determined by the thermal under-cooling (ATcell) in that cell and the state of the 26 surrounding cells. If the size shrinks to zero, the cell turns into a liquid state and the octahedron is deleted. The octahedron is also deleted when the cell turns solid. The deletion happens when the octahedron cannot grow or is surrounded by solid neighbors. The octahedron is also deleted when the random turbulence in the fluid hydrodynamics may turn a CA cell into a non-CA material.

[0112] The octahedron growth dynamics is determined by evaluating a velocity at each vertex defined along the diagonals and is a direct function of the local value of ATcell, and it is also indirectly related to the local thermal gradient vector which depends on the temperature variations which will extend beyond the immediate neighboring cells. Each cell that has octahedra whose diagonals point respectively in the same direction (referred to as crystallographic orientation) belong to the same grain defined by a unique index. Grains with different orientations will have many cells with octahedra pointing (diagonals) in different directions. The CA algorithm implicitly will favor the fast growth of octahedra whose diagonal directions are oriented parallel to the thermal gradient, which is a desirable physical behavior. These octahedra will be able to capture faster their nearest neighbors.

[0113] The capturing rules are expensive to evaluate and follow the decentered-octahedron algorithm. These capture rules define another underlying dynamical system, other than the laser heating driving the fluid flow and material phase change, with which solidification takes place. As an octahedron reaches a specific size, its geometric faces will envelope the center of the neighboring cell(s). When this happens, the cell(s) in question will be captured. As soon as a cell is captured, a new octahedron takes birth and will inherit the properties of the capturing octahedron such as orientation, some initial size computed by the capture algorithm and the unique grain index to which that octahedron belonged to. The captured cell state turns from liquid to mushy (region between solid and liquid cells).

[0114] In step 304, the neural network ingests the training data, in some embodiments, simulation results were post-processed using the Visit software to interpolate the adaptive unstructured grid simulations down onto a coarser grid than that required by LLRT. As part of the post-process, simulation results are run through material interface reconstruction to maintain conservation of mass during coarsening while preserving continuity of material interfaces. A 3D Gaussian blur is also applied to the laser energy deposition to smooth out numerical artifacts, and then scaled by the total 339596161.1laser energy at that point in time. A binary mask of the material surface is further created at each timestep.

[0115] T raining utilized four tensors at each time point. Specifically, adhering to a metal surface metal volume fraction, temperature, local laser energy and a mask made of the metal-air interface using the volume fraction data, the disclosed network takes volume fraction and temperature as input, and outputs energy deposited. The mask is used to accept network outputs on the surface interface. The model received an input 3D tensor with two channels (material fraction and temperature). The output is a 3D tensor with one channel: the total energy deposited into that point. The surface mask is used when calculating loss and was never seen by the model. Data was normalized by scaling all inputs so that the standard deviation was approximately 1.

[0116] In some embodiments, a squeeze U-net design is implemented for the first neural network (referred to elsewhere above) based on a physical intuition that laser irradiance at a single voxel depends on global geometry everywhere due to reflections. Further, the Squeeze U-Net network design architecture compresses the complex global geometry into a smaller basis that the network uses to estimate global geometry. At each layer of the outermost network, the problem extents are down sampled by half in each dimension. Enough layers were added to the network until the entire problem was reduced to a small 33 grid or smaller.

[0117] Design deviates from a standard squeeze U-net by roughly increasing number of channels in each layer of the network by a factor of a square root of 2 instead of a factor of 2. This deviation reduced the memory footprint and drastically improved network performance. On most modern computers, the memory footprint of the model is such that is the model is fully in-memory. The small memory footprint provides useful performance benefits. Batch norms were interspersed between “Fire” convolutional layers from the original squeezenet paper, and each Fire module’s squeeze was set to 1 / 3 of that Fire module’s output. Designed network down samples are done via a 2A3 max pool kernel, and up samples were handled with simple linear interpolation between layers. The final full convolutional net had ~71k free parameters.

[0118] Training loss was given by the following equation:

[0119] Loss(y, y*,m) = Sum|(y - y*) • m| / Sum(m) + | Sum(y) • m - Sum(y*) • m|

[0120] A binary mask m of the material interface is employed to discard network outputs where the laser cannot deposit energy - i.e., within air or within the bulk interior.349596161.1LLNL-077518-8097. WG00On the material surface interface, the model employs a simple point-wise mean L1 loss at each timestep. The model computes a mean within each timestep to ensure that all timesteps were weighted evenly during training (i.e. timesteps with a larger surface area should not be over-emphasized by the loss function). The function further includes a global conservation loss term to ensure that the total predicted energy deposited on the material interface was accurate. The total energy deposited by the laser determines the global temperature for subsequent timesteps, affecting conservation of energy and numerical stability. Based on various embodiments, multiple, separate networks are trained specific to each embodiment, splitting the data up 90%-10% between training and validation. Training and validation losses are of roughly equivalent magnitude for each network.

[0121] Referring again to use of the CA as discussed above in step 202, singlechannel snapshots of the polycrystalline structure are generated by defining <|)(r) = LNi=1 r)3l (r) as the order parameter <|> so that is close to 0 in the grain boundary region and 1 inside grains. The spatial grid of was down sampled spatially by a factor of 4A2 times from 256A2 to 64A2 and temporally 80 times, i.e., 80 PDE time steps correspond to one GNN time step. In 3D, the down sampling ratio was 4A3 spatially and 1000 temporally. Therefore, the data consists of time series of coarse-grained arrays for the field 0t is an element of RNxxNy (xNz )xNc where Nx / y / z =64 (2D) or 32 (3D) is the spatial grid size and Nc = 1 is the number of channels. The grid size is chosen to be large enough to accommodate sufficient variation in mi era structure configurations and also provides adequate resolution to resolve interfaces in microstructure with at least 1-2 pixels. The model is implemented in PyTorch and trained on 2 NVidia V100 or 4 480-Ti GPUs with single (32-bit) floating-point precision. Typical training time is 10 hours, with an initial learning rate of 10A-3 that gradually decays to 10A-6.

[0122] In ingesting the data, there is no presumption of explicit history dependence, assuming that the next time step is only dependent on the current, not previous steps. Given current 0t, the next frame 0“t+1 is predicted by: 0"t+1 = G(0t) + 0t. The time evolution predictions are then performed autoregressively. Some embodiments largely adopt MeshGraphNet, a type of message-passing graph neural network. These embodiments of the network used 64 hidden features. The neural network operators are built from multi-layer perceptrons with two hidden layers and layer normalization between them. The model includes message passing layers that operate sequentially on the laten edge and vertex features of the network. The message passing steps enable the GNN to transmit and aggregate information along connected edges, and each additional 359596161.1LLNL-077518-8097. WG00message-passing layer builds up a more complex dependence on vertices farther away. The number of message-passing layers K required to obtain accurate predictions is then related to a few factors, including the effective instantaneous interaction distance, and the levels of spatial and temporal downs-sampling.

[0123] In relevant embodiments, the model consists of three modules, implemented as different nodal output channels of the GNN’s decoder, and three corresponding loss functions. The first module is a cell state classifier SO to predict the state (0, 1 2 corresponding to liquid, mushy and solid state) of a non-vacuum cell at the next timestep. The outputs of S0(x) for each cell x are three logits subject to the cell classification loss using cross entropy (CE) loss Loss(sta) = CE(S0(x) (x), s(x)) where s(x) is the ground truth state of cell x at t + 1 .

[0124] Second, a regression model O0(x) to predict the octahedron life on the next timestep for a current mushy cell. The regression model is trained with a L2 or mean square error (MSE) loss L(oct) = ||O0(x)(x) - o(x)||A2 where o(x) is the ground truth octahedron life of cell x at t + 1.

[0125] The third module C outputs 26 logits representing 26 neighbors of a liquid cell, and compare them to the ground truth label by which of these 26 neighbors is the cell captured Loss(cap) = CE(C0(x)(x), <5(grain(t, x), grain(t + 1, nb(x)))). In the inference stage, the next state of each cell with active material is predicted by the classifier S0(x), and cells predicted to be mushy will be updated to new octahedral life O0(x). Cells that experienced a capture event (state transitioning from 0 to 1 or 2) will be associated with the grain identifier of the neighbor argmax(C0(x)).In step 306, once trained the model(s) receive input queries (including process variables and printer instructions) which are passed between the models to generate a microstructure. The computational expense of output of the neural network is significantly lower than a laser ray tracing simulator that is assigned to execute a full microstructure itself. The neural network being trained on laser ray tracing simulations provides an accurate simulation of the simulation and does so faster and with less computational expense. The generation of AM workpiece microstructures is vastly improved over existing platforms in that it is generated more quickly and without as heavy a processor burden.

[0126] FIG. 4 is a flow diagram of modification of additive manufacturing printer instructions in accordance with some example embodiments. In step 402, the neural network as described above outputs a microstructure of a workpiece associated with a set of printer instructions. The micro structure is a digital twin of the workpiece and 369596161.1supports CAD structural testing such as Structural simulation, Stress analysis, Flow simulation, Finite element analysis (FEA), Computational fluid dynamics (CFD), Multibody dynamics (MBD). On market products such as Autodesk® perform tests such as those referenced above. In addition to structural tests, the microstructure evidences errors in AM printer instructions. The errors are identifiable via user operation and review, via printer management software, or machine learning (ML) model designed to identify errors.

[0127] In step 404, the above-described tests or checks are performed on the digital twin of the workpiece. In step 406, modifications are made to the AM printer instructions. The modifications revise the instructions to change process variables or add / remove material applications to determined positions on the (complex) geometry of the workpiece. The manner in which the AM printer instructions are changed includes user operation and review, printer management software, or machine learning (ML) model designed to correct errors. Through use of the above-described digital twin generation method and system a user arrives at and is enabled to conduct step 406 with greater ease than previous. The field of rapid prototyping and design is thus improved. In step 408, modified AM printer instructions are transmitted to the AM printer and the printer generates a physical copy of the workpiece.

[0128] Application of the method of Figure 4 is implemented in steps including user intervention and review or is fully automated. Further, in situ modifications and tests are applicable dynamically throughout printing. Where the digital twin plots out the next segment of printing (e.g., next few instructions, next few seconds or minutes of printing) tests are performed on that digital twin, and revisions to instructions are generated as the print is happening allowing for real-time adaptation and improved accuracy in predicting outcomes. Dynamic changes to instructions in situ enable prevention of cascading issues that cause small errors to accumulate over the course of multiple AM printer actions as well as other mid-print issues.

[0129] ML System

[0130] FIG. 5 is a block diagram illustrating an example ML system 500, in accordance with one or more embodiments. The ML system 500 can implement one or more components of the computer systems and apparatuses discussed herein and can be deployed in-the-loop with a time-stepping multiphysics simulation of an additive manufacturing (AM) process, such as laser powder bed fusion (LPBF) or directed energy deposition (DED). Although illustrated in a particular configuration, different embodiments of the ML system 500 include different and / or additional components and are connected 379596161.1in different ways. The ML system 500 is sometimes referred to as an ML module.

[0131] The ML system 500 includes a feature extraction module 508 implemented using components of an example computer system, as described herein. In some embodiments, the feature extraction module 508 extracts a feature vector 512 from input data 504. The input data 504 comprises one or more simulation snapshots generated by a high-fidelity AM digital twin (e.g., a coupled multiphysics solver with a ray-tracing energy-deposition solver), where each simulation snapshot corresponds to a simulation time step, beam position, or solver cycle. In some embodiments, the simulation snapshot includes at least (i) a material-distribution field (e.g., a metal volume-fraction field) representing an evolving metal-gas interface and (ii) a thermal-state field (e.g., a temperature field), and may further include one or more process descriptors (e.g., beam power, scan speed, spot size, or scan direction). The feature vector 512 includes features 512a, 512b, . . ., 512n derived from the simulation snapshot, such as local interface indicators, local interface geometry descriptors, thermal gradients or cooling-rate proxies, and / or localized beam-parameter encodings.

[0132] In some embodiments, the feature extraction module 508 reduces redundancy in the input data 504, for example repetitive or correlated values across neighboring voxels or cells, to transform the input data 504 into the reduced set of features 512. The feature vector 512 contains information relevant to predicting AM energy coupling and downstream outcomes, such that events or data value thresholds of interest are identified by the ML model 516 using a reduced representation. In some example embodiments, dimensionality reduction techniques used by the feature extraction module 508 include principal component analysis (PCA), autoencoders, and deep feature synthesis. In alternative embodiments, the ML model 516 performs deep learning directly on the input data 504 to learn data representations, as opposed to using task-specific algorithms. In such embodiments, no explicit feature extraction is performed and the features 512 are implicitly extracted by the ML system 500.

[0133] In alternative example embodiments, the ML model 516, for example in the form of a convolutional neural network (CNN) or three-dimensional fully convolutional encoder-decoder network, generates output 524 without an explicit feature extraction stage, directly from the input data 504. In some embodiments, the output 524 includes a predicted absorbed energy deposition field and / or a predicted absorptivity (coupling) value for the AM process at the simulation snapshot. In some embodiments, the output 524 is provided to the computer device 528 and / or to a multiphysics solver as a heatsource term that advances a subsequent simulation time step. The computer device 528389596161.1is a server, computer, tablet, smartphone, workstation, or high-performance computing (HPC) node, implemented using components of an example computer system, as described herein. In some embodiments, the steps performed by the ML system 500 are stored in memory on the computer device 528 for execution.

[0134] A CNN is a type of feed-forward artificial neural network in which the connectivity pattern between its neurons is inspired by the organization of a visual cortex. In embodiments, the ML model 516 is a CNN that includes convolutional layers and optionally pooling and / or strided convolution layers. In some embodiments, the architecture of the ML model 516 is “fully convolutional,” which means that variable-sized simulation tensors and / or patches can be fed into it. In some embodiments, the ML model 516 operates on three-dimensional tensors corresponding to local volumetric patches centered on a beam position or region of interest, and outputs a three-dimensional field aligned to the same grid or discretization used by the simulation snapshot.

[0135] In some embodiments, the ML system 500 trains the ML model 516 based on training data 520 to correlate the feature vector 512 (and / or the raw input data 504) to expected outputs in the training data 520. The training data 520 comprises a plurality of simulation snapshots produced by one or more high-fidelity AM simulations, where each training example includes input fields (e.g., temperature and material distribution) and one or more ground-truth targets (e.g., a ray-traced absorbed energy deposition field and / or a ground-truth absorptivity / coupling value). In some embodiments, the training data 520 is split into a training set and a validation set 532 by assigning a first portion of simulation snapshots to training and holding out a second portion of simulation snapshots for validation.

[0136] In embodiments, the ML system 500 uses supervised ML to train the ML model 516. In some embodiments, the ML system 500 applies one or more loss terms that quantify prediction error relevant to AM energy coupling and simulation stability, including: (i) absorptivity error between a predicted absorptivity (or coupling efficiency) and a ground-truth absorptivity (or coupling efficiency); (ii) interface-local reconstruction error between a predicted absorbed energy deposition field and a ground-truth absorbed energy deposition field evaluated preferentially at or near an evolving metal-gas interface, such as an interface L1 error; (iii) a conserved energy error term that penalizes mismatch between a total predicted absorbed energy and a total ground-truth absorbed energy fora simulation snapshot; and (iv)one or more downstream error terms computed by propagating the predicted deposition into a thermal / melt-pool update and comparing a resulting melt pool descriptor (e.g., melt pool depth, width, length, boundary, or volume)399596161.1to a ground-truth melt pool descriptor, such as a downstream melt pool geometry error. In some embodiments, the ML system 500 iteratively retrains the ML model 516 until a stopping condition occurs, such as a validation criterion indicating that the ML model 516 satisfies one or more accuracy and / or stability requirements for in-the-loop deployment.

[0137] In some embodiments, the validation set 532 includes simulation snapshots corresponding to held-out geometries, held-out scan strategies, and / or held-out process windows that were not used in training, and the ML system 500 applies the trained ML model 516 to the validation set 532 to quantify generalization. In embodiments, the accuracy measurement reported for the validation set 532 includes one or more of: absorptivity error, interface L1 error, conserved energy error, and downstream melt pool geometry error. In some embodiments, the ML system 500 stores or reports these validation metrics to determine whether the ML model 516 is sufficiently accurate and stable for deployment as a surrogate that replaces or accelerates high-fidelity energydeposition simulation within an AM digital twin workflow.Computing System

[0138] Figure 6 is a block diagram illustrating an example computer system 600, in accordance with one or more embodiments. At least some operations described herein are implemented on the computer system 600. The computer system 600 includes one or more central processing units (“processors”) 602, main memory 606, non-volatile memory 610, network adapters 612 (e.g., network interface), video displays 618, input / output devices 620, control devices 622 (e.g., keyboard and pointing devices), drive units 624 including a storage medium 626, and a signal generation device 630 that are communicatively connected to a bus 616. The bus 616 is illustrated as an abstraction that represents one or more physical buses and / or point-to-point connections that are connected by appropriate bridges, adapters, or controllers. In embodiments, the bus 616 includes a system bus, a Peripheral Component Interconnect (PCI) bus or PCI-Express bus, a HyperTransport or industry standard architecture (ISA) bus, a small computer system interface (SCSI) bus, a universal serial bus (USB), an IIC (I2C) bus, or an IEEE standard 1394 bus (also referred to as “Firewire”).

[0139] In embodiments, the computer system 600 shares a similar computer processor architecture as that of a desktop computer, tablet computer, personal digital assistant (PDA), mobile phone, game console, music player, wearable electronic device (e.g., a watch or fitness tracker), network-connected (“smart”) device (e.g., a television or home assistant device), virtual / augmented reality systems (e.g., a head-mounted display), or another electronic device capable of executing a set of instructions 409596161.1(sequential or otherwise) that specify action(s) to be taken by the computer system 600.

[0140] While the main memory 606, non-volatile memory 610, and storage medium 626 (also called a “machine-readable medium”) are shown to be a single medium, the terms “machine-readable medium” and “storage medium” should be taken to include a single medium or multiple media (e.g., a centralized / distributed database and / or associated caches and servers) that store one or more sets of instructions 628. The terms “machine-readable medium” and “storage medium” shall also be taken to include any medium that is capable of storing, encoding, or carrying a set of instructions for execution by the computer system 600.

[0141] In general, the routines executed to implement the embodiments of the disclosure are implemented as part of an operating system or a specific application, component, program, object, module, or sequence of instructions (collectively referred to as “computer programs”). The computer programs typically include one or more instructions (e.g., instructions 604, 608, 628) set at various times in various memory and storage devices in a computer device. When read and executed by the one or more processors 602, the instruction(s) cause the computer system 600 to perform operations to execute elements involving the various aspects of the disclosure.

[0142] Moreover, while embodiments have been described in the context of fully functioning computer devices, those skilled in the art will appreciate that the various embodiments are capable of being distributed as a program product in a variety of forms. The disclosure applies regardless of the particular type of machine or computer-readable media used to actually effect the distribution.

[0143] Further examples of machine-readable storage media, machine-readable media, or computer-readable media include recordable-type media such as volatile and non-volatile memory 610, floppy and other removable disks, hard disk drives, optical discs (e.g., Compact Disc Read-Only Memory (CD-ROMS), Digital Versatile Discs (DVDs)), and transmission-type media such as digital and analog communication links.

[0144] The network adapter 612 enables the computer system 600 to mediate data in a network 614 with an entity that is external to the computer system 600 through any communication protocol supported by the computer system 600 and the external entity. In embodiments, the network adapter 612 includes a network adapter card, a wireless network interface card, a router, an access point, a wireless router, a switch, a multilayer switch, a protocol converter, a gateway, a bridge, a bridge router, a hub, a digital media receiver, and / or a repeater.

[0145] In embodiments, the network adapter 612 includes a firewall that governs 419596161.1and / or manages permission to access proxy data in a computer network and tracks varying levels of trust between different machines and / or applications. In embodiments, the firewall is any number of modules having any combination of hardware and / or software components able to enforce a predetermined set of access rights between a particular set of machinesand applications, machinesand machines, and / or applications and applications (e.g., to regulate the flow of traffic and resource sharing between these entities). The firewall additionally manages and / or has access to an access control list that details permissions including the access and operation rights of an object by an individual, a machine, and / or an application, and the circumstances under which the permission rights stand.

[0146] In embodiments, the functions performed in the processes and methods are implemented in differing order. Furthermore, the outlined steps and operations are only provided as examples. For example, some of the steps and operations are optional, combined into fewer steps and operations, or expanded into additional steps and operations without detracting from the essence of the disclosed embodiments.

[0147] In embodiments, the techniques introduced here are implemented by programmable circuitry (e.g., one or more microprocessors), software and / or firmware, special purpose hardwired (i.e. , non-programmable) circuitry, or a combination of such forms. In embodiments, special-purpose circuitry is in the form of one or more applicationspecific integrated circuits (ASICs), programmable logic devices (PLDs), field-programmable gate arrays (FPGAs), etc.

[0148] The description and drawings herein are illustrative and are not to be construed as limiting. Numerous specific details are described to provide a thorough understanding of the disclosure. However, in certain instances, well-known details are not described in order to avoid obscuring the description. Further, various modifications can be made without deviating from the scope of the embodiments.

[0149] The terms used in this specification generally have their ordinary meanings in the art, within the context of the disclosure, and in the specific context where each term is used. Certain terms that are used to describe the disclosure are discussed above, or elsewhere in the specification, to provide additional guidance to the practitioner regarding the description of the disclosure. It will be appreciated that the same thing can be said in more than one way. One will recognize that “memory” is one form of a “storage” and that the terms are on occasion used interchangeably.

[0150] Consequently, alternative language and synonyms are used for any one or more of the terms discussed herein, and no special significance is to be placed upon 429596161.1LLNL-077518-8097. WOOOwhether or not a term is elaborated or discussed herein. Synonyms for certain terms are provided. A recital of one or more synonyms does not exclude the use of other synonyms. The use of examples anywhere in this specification, including examples of any term discussed herein, is illustrative only and is not intended to further limit the scope and meaning of the disclosure or of any exemplified term. Likewise, the disclosure is not limited to various embodiments given in this specification.439596161.1

Claims

LLNL-077518-8097. WOOOCLAIMS1. A computer-implemented method of operating a time-stepping multiphysics simulation of a laser-based additive manufacturing process, the method comprising:receiving, for a build region discretized on a three-dimensional computational grid at a simulation time step, (i) a metal material-distribution field representing at least an evolving metal-gas interface and (ii) a temperature field;computing, from the metal material-distribution field, an interface mask that identifies grid cells corresponding to the metal-gas interface;executing, at the simulation time step, a trained three-dimensional convolutional neural network that takes as input the metal material-distribution field and the temperature field and outputs a predicted absorbed laser energy deposition field on the three-dimensional computational grid;enforcing physical admissibility of the predicted absorbed laser energy deposition field by applying the interface mask to suppress predicted deposition outside the metal-gas interface;using the physically admissible absorbed laser energy deposition field as a heat-source term in the multiphysics simulation to update the temperature field for a subsequent simulation time step; andrepeating the executing, enforcing, and using steps for a plurality of simulation time steps to reduce wall-clock runtime of the multiphysics simulation relative to executing a laser ray tracing solver at the plurality of simulation time steps.449596161.1LLNL-077518-8097. WOOO2. A system configured to accelerate a coupled laser ray-tracing and multiphysics simulation of a laser-based additive manufacturing process, the system comprising:one or more processors; andmemory storing instructions that, when executed by the one or more processors, cause the one or more processors to:(i) obtain, at successive simulation time steps, a metal material-distribution field and a temperature field for a build region;(ii) derive, at each of the successive simulation time steps, an interface mask identifying metal-gas interface locations from the metal material-distribution field;(hi) execute a trained three-dimensional encoder-decoder convolutional neural network with skip connections to generate a predicted absorbed laser energy deposition field from the metal material-distribution field and the temperature field;(iv) apply the interface mask to the predicted absorbed laser energy deposition field to generate a physically admissible absorbed laser energy deposition field; and (v) couple the physically admissible absorbed laser energy deposition field into a time-stepping multiphysics solver to update the temperature field and at least one melt pool descriptor,wherein the instructions further cause the one or more processors to maintain numerical stability of the time-stepping multiphysics solver by constraining deposition to the metal-gas interface via the interface mask at the successive simulation time steps.

3. A non-transitory computer-readable medium storing instructions that, when executed by one or more processors, cause the one or more processors to train 459596161.1LLNL-077518-8097. WOOOand deploy an energy-deposition surrogate that replaces repeated laser ray tracing calls in a time-stepping multiphysics simulation, by:generating training examples by executing a laser ray tracing solver to compute, for each of a plurality of simulation snapshots, a ray-traced absorbed laser energy deposition field corresponding to an evolving metal-gas interface;for each training example, deriving an interface mask from a corresponding metal material-distribution field:training a three-dimensional convolutional neural network to output a predicted absorbed laser energy deposition field from at least the metal materialdistribution field and a corresponding temperature field by minimizing an objective function that includes (i) an interface-restricted voxelwise error term computed using the interface mask and (ii) a global absorbed-energy conservation term that penalizes mismatch between a total predicted absorbed energy and a total ray-traced absorbed energy summed over interface locations identified by the interface mask; and deploying the trained three-dimensional convolutional neural network in the time-stepping multiphysics simulation by applying the interface mask during inference to generate a physically admissible absorbed laser energy deposition field that is used as a heat-source term to advance the time-stepping multiphysics simulation.

4. The method of claim 1, wherein the interface mask is generated by thresholding a metal volume fraction field and selecting grid cells that satisfy a metal-to-gas transition criterion based on neighboring grid cells.469596161.1LLNL-077518-8097. WOOO5. The method of claim 1, further comprising enforcing non-negativity of the physically admissible absorbed laser energy deposition field by clamping negative predicted deposition values to zero after applying the interface mask.

6. The method of claim 1. wherein executing the trained three-dimensional convolutional neural network comprises executing a memory-efficient squeeze U-net architecture comprising fire modules.

7. The method of claim 6, wherein a number of feature channels increases by approximately ^2 per downsampling level of the squeeze U-net.

8. The method of claim 1, wherein the trained three-dimensional convolutional neural network is executed on a central processing unit in the same address space as the multiphysics solver to reduce data movement overhead during the plurality of simulation time steps.

9. The method of claim 1, wherein the trained three-dimensional convolutional neural network is executed on a graphics processing unit and an output deposition field is transferred to the multiphysics solver for the subsequent simulation time step.

10. The method of claim 1, wherein the multiphysics simulation includes at least one of conduction, convection, radiation, surface tension, recoil pressure, or phase change, and the heat-source term is applied as a volumetric source in grid cells identified by the interface mask.479596161.1LLNL-077518-8097. WOOO11. The method of claim 1, further comprising preprocessing a training deposition field used to train the trained three-dimensional convolutional neural network by smoothing the training deposition field to reduce ray sampling noise and rescaling the smoothed field to preserve a timestep absorbed-energy budget.

12. The method of claim 1, wherein the build region is represented on a uniform grid for inference and the multiphysics solver operates on an adaptive or unstructured discretization, and further comprising interpolating the metal material-distribution field and the temperature field to the uniform grid before executing the trained three-dimensional convolutional neural network and mapping the physically admissible absorbed laser energy deposition field back to the adaptive or unstructured discretization.

13. The method of claim 1, further comprising computing, at a simulation time step, a consistency measure based on a difference between (i) a total absorbed energy implied by the physically admissible absorbed laser energy deposition field and (ii) an absorbed-energy expectation derived from beam power, and invoking a laser ray tracing solver for the simulation time step when the consistency measure exceeds a threshold.

14. The method of claim 13, further comprising replacing, for the simulation time step, at least a portion of the physically admissible absorbed laser energy deposition field with a ray-traced absorbed laser energy deposition field while489596161.1LLNL-077518-8097. WOOOcontinuing to use the trained three-dimensional convolutional neural network at other simulation time steps.

15. The method of claim 1, wherein the laser-based additive manufacturing process comprises laser powder bed fusion and the metal material-distribution field represents a powder-and-solid distribution in a powder bed.

16. The method of claim 1, wherein the laser-based additive manufacturing process comprises directed energy deposition and the metal material-distribution field represents a deposited powder stream and a melt pool surface.

17. The system of claim 2, wherein the instructions further cause the one or more processors to cache the interface mask for a plurality of beam positions within a scan segment and reuse the cached interface mask while the metal materialdistribution field remains unchanged within a tolerance.

18. The non-transitory computer-readable medium of claim 3, wherein the global absorbed-energy conservation term comprises an absolute difference between a sum of predicted deposition values over interface locations and a sum of ray-traced deposition values over the interface locations.

19. The non-transitory computer-readable medium of claim 3, wherein the interface-restricted voxelwise error term comprises an LI error normalized by a count of interface locations indicated by the interface mask.499596161.1LLNL-077518-8097. WOOO20. The system of claim 2, wherein the at least one melt pool descriptor comprises a melt pool boundary, melt pool depth, melt pool width, or melt pool volume computed from the updated temperature field.509596161.1

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