85 results about "Automatic differentiation" patented technology

The present disclosure provides a computer-implemented system for automated augmentation of differential equation models. The system stores differential equations representing mechanistic behavior of physical or computational processes and constructs a hybrid computational solver by embedding a trainable universal approximator with adjustable parameters into the differential equations, where approximator outputs augment time derivatives during numerical integration. An iterative training process adjusts parameters through numerical integration, monitors integration failures, assigns infinite penalty values to loss functions when failures occur, and computes gradients using automatic differentiation otherwise. The system computes sensitivity metrics via Jacobian matrix evaluation, classifies input / output subsets as significant based on threshold-exceeding sensitivity metrics, generates a reduced approximator operating on classified subsets, and replaces the universal approximator with the reduced version to create an optimized solver.

The invention relates to the technical field of metal composite materials, in particular to a metal composite material production process dynamic simulation method based on digital twinning. Comprising the following steps: constructing a digital twin model comprising a physical entity layer, a virtual model layer and a connection layer, and establishing a Fourier neural operator model embedded with a Navier Stokes equation and a heat conduction equation constraint; real-time molten pool monitoring data are mapped into model input through a connecting layer, and advanced time step deduction is executed by using a deep learning model to predict the state of a molten pool; based on the differentiable characteristic of a physical information neural operator, calculating the gradient of a prediction state and an ideal target by using an automatic differential algorithm, generating a process parameter field through reverse iteration updating, and discretizing the process parameter field into a galvanometer control instruction; and when the risk of aggregation of the reinforced phase particles is predicted to exist, automatically generating a swing scanning strategy to realize active suppression. The method gives consideration to simulation precision and real-time performance.

The invention discloses a physical model discovery and reconstruction method for light beam transmission characteristics based on a sparse physical information neural network, and belongs to the technical field of nonlinear optics and deep learning intersection, and the method comprises the following steps: S1, making a sparse and low-fidelity data set; s2, establishing a candidate function library of items possibly existing in a data back model by using automatic differentiation; S3, constructing a physical information neural network model with sparse regression to discover a physical model structure; s4, coefficient fine tuning is carried out on the found physical model, and high-fidelity data is reconstructed.The method is suitable for model discovery of light beam transmission data supported by a constant coefficient or variable coefficient partial differential equation, scarce and noisy low-fidelity data can be utilized, and high-fidelity data can be obtained. A simple physical model is found according to a physical information neural network and sparse regression, and a light beam transmission dynamic process is reconstructed, so that subsequent theoretical analysis and research on light beam transmission characteristics are facilitated.

The invention belongs to the technical field of aero-engine design, and provides a sliding bearing lubrication gap prediction method based on a PINN neural network, and the method comprises the steps: generating a training data set of the PINN neural network, constructing the PINN neural network, employing a reverse mechanism of the neural network, calculating a partial differential operator through automatic differential, and carrying out the prediction of the lubrication gap of a sliding bearing. Customizing a dynamic pressure lubrication Reynolds equation into a loss function in a deep learning framework; and a prediction data set of the neural network model is generated, the trained PINN model and weight parameters are loaded, construction of a prediction model is completed, and an oil film pressure distribution curved surface is generated. According to the method, the accuracy of oil film pressure distribution calculation is remarkably improved, and meanwhile, the speed of numerical calculation can be remarkably increased.

The invention relates to the technical field of environment monitoring, and particularly discloses an air quality prediction optimization method and system based on deep learning, a space-time diagram structure is constructed by taking a monitoring station as a node, pollutant concentration, meteorological elements and geographic coordinates are fused to form node features, and a dynamic adjacency matrix is generated based on real-time wind direction and wind speed; spatial dependency feature representation is obtained through multi-level spatial feature aggregation; after a prediction concentration field is obtained through feature mapping, spatial gradient and curvature features are calculated through the automatic differential technology, the relative contribution degree of the advection transmission and diffusion process is analyzed in combination with wind field data, the consistency of a prediction result and a physical rule is verified, and a physical consistency residual error is obtained; a composite optimization target is constructed based on the data fitting difference and the physical consistency residual error, and parameter configuration meeting physical rule constraints is obtained through alternate optimization; and finally, processing real-time monitoring data by using the optimized parameters, and outputting an air quality prediction result conforming to a physical rule.

A method for evaluating and / or adapting one or more technical models related to an industrial and / or technical process, as well as a corresponding system and computer program are provided. The method comprises obtaining (S1) a fully or partially non-causal modular parametric model of the industrial and / or technical process, the parametric model comprising at least one physical sub-model and at least one neural network sub-model, including obtaining one or more parameters of the parametric model. The method further comprises generating (S2) a system of differential equations based on the parametric model, and simulating (S3) dynamics of one or more states of the industrial and / or technical process over time based on the system of differential equations. The method also comprises applying (S4) reverse mode automatic differentiation to the system of differential equations while simulating the industrial and / or technical process to generate an estimate representing an evaluation of the industrial and / or technical process model.

The application discloses a method for discovering control equations from scarce and noisy data based on physics. The application combines a physical information neural network and a sparse regression method to discover the partial differential control equations of a dynamic system from scarce and noisy data. Firstly, the size of the candidate function library is effectively reduced through a dimension verification method. Then, the powerful nonlinear fitting capability and automatic differentiation characteristics of a deep neural network are used to model a physical system and calculate candidate functions. Finally, the form of the control equation and the coefficients of the equation are obtained through sparse regression, and the coefficients are fine-tuned through a DNN. The method can not only discover control equations from data, but also obtain a network model to realize response prediction of a dynamic system. The method is simple, efficient, high-precision and highly universal, and can be widely applied to physical knowledge mining, modeling and reasoning of complex dynamic systems.

The invention discloses a weighted exponential decay instantaneous phase inversion method based on automatic differentiation. Under the framework of automatic differential, the underground velocity model can be inversed by using phase and waveform information at the same time, and the advantages of constructing an initial model at the early stage of inversion and improving the resolution of the model at the later stage of inversion are combined. The method comprises the following steps: firstly, performing Hilbert transform on seismic wave data, extracting index instantaneous phase information of observation data and simulation data, and constructing a weighted instantaneous phase inversion objective function by introducing an attenuation coefficient and combining waveform information; secondly, carrying out back propagation on the loss of the objective function based on an automatic differential framework, and solving an update gradient; and finally, updating the speed model by using an SDG optimizer. According to the method, a layered multi-scale inversion effect can be realized by adjusting attenuation factor values, an objective function is constructed by weighting exponential attenuation phase information and waveform information, a better initial model is constructed before a conventional multi-scale full-waveform inversion process, the problem of cycle jump of full-waveform inversion is relieved, and the inversion efficiency is improved. And finally, a high-precision inversion result is obtained.

A digital twin modeling method and device for motors based on multi-field coupled PINN (Partial Differential Equations) belongs to the field of intelligent manufacturing and advanced control technology for motors. Its key features include: acquiring stator current, voltage, rotor position, and vibration signals of the motor to construct a full-domain multimodal sensing layer; constructing a multi-field coupled PINN model based on automatic differentiation; and embedding the multi-field partial differential equations (PDEs) inside the motor as prior knowledge into the network structure of the PINN model. By utilizing PINN technology, the physical laws of PDEs are integrated into the neural network, ensuring both millisecond-level inference speed and physical consistency in areas lacking sensor data, achieving both high fidelity and real-time performance. It enables precise virtual sensing of unmeasurable rotor permanent magnet temperature and local magnetic flux density saturation within the motor, achieving full-domain observability. Through edge-cloud collaboration, it can automatically evolve as the physical entities of the motor age (e.g., resistance changes, magnet demagnetization), maintaining model accuracy throughout its entire lifecycle.

Examples including a system described herein implement a novel liquid time constant neural network (LTC-NN) based architecture to recover an underlying model of physical dynamics from real world data. The automatic differentiation property of LTC-NN nodes overcomes problems associated with low sampling rate, the input dependent time constant in the forward pass of the hidden layer of LTC-NN nodes creates a massive search space of implicit physical dynamics, the physics model solver based data reconstruction loss guides the search for the correct set of implicit dynamics, and drop out in dense layer ensures extraction of the sparsest model. Further, to account for perturbation timing error, the LTC-NN based architecture of the system utilizes dense layer nodes to search through input shifts that results in the lowest reconstruction loss.

The application discloses a steel bridge deck roller compacted asphalt concrete construction simulation method based on BIM, and relates to the technical field of simulation. The method first analyzes the geometric boundary of the BIM model and constructs an adaptive space-time sampling point set; then constructs a deep neural network introducing Fourier feature mapping, maps low-dimensional space-time coordinates into high-dimensional features to capture high-frequency physical changes; then establishes a composite loss function containing heat conduction, thermal coupling and boundary condition residual error, and uses automatic differentiation technology and an adaptive weight algorithm based on gradient statistics for unsupervised training; finally, the trained lightweight model is integrated into the BIM rendering engine. The application solves the problems of long time consumption of traditional finite element simulation calculation, inability of real-time interaction, and poor generalization ability of pure data-driven AI due to lack of internal measured data, and realizes real-time, high-precision dynamic simulation of the temperature field and stress field of the steel bridge deck pavement.

This invention discloses a method and system for solving the performance of a gas turbine engine by integrating differentiable operators and static computation graphs. The method includes: constructing differentiable component operators: reconstructing the input-output mapping relationship of the core components of the gas turbine engine into a globally differentiable surrogate model, which possesses analytical gradient solving capability; constructing the overall engine static computation graph: utilizing a programming framework supporting automatic differentiation, establishing a general graph construction mechanism decoupled from the engine topology, which automatically instantiates the corresponding static computation graph based on the input engine topology description; and reverse-mode automatic differentiation solving: calculating the residual vector through forward propagation, and using reverse-mode automatic differentiation technology to propagate the gradient flow backward along the static computation graph, analytically obtaining the Jacobian matrix required for Newton iteration, and completing the solution of the engine's overall performance residual equation. This invention achieves efficient, accurate, and stable simulation of gas turbine engine performance.

The invention discloses a complex river network flow prediction method based on a diffusion space-time diagram neural network guided by physical information, and relates to the technical field of intelligent water conservancy and hydrological time sequence prediction. According to the method, a diffusion space-time diagram neural network (PI-Diffusion STG) guided by physical information is constructed aiming at the problems of lack of physical consistency and insufficient long-distance space-time dependence capture capability of an existing data-driven model. According to the model, a bidirectional graph diffusion convolution module is designed, forward-flow hydraulic conduction and reverse-flow jacking effects in a river network are simulated through forward diffusion and backward diffusion respectively, and bidirectional spatial-temporal characteristics are effectively extracted; performing multi-step traffic prediction by adopting a sequence-to-sequence architecture; meanwhile, a Saint-Venant equation set describing fluid mechanics is used as a physical constraint regularization term to be deeply fused into a loss function, and a physical residual error is calculated by utilizing a hybrid strategy combining automatic differential and finite difference on a graph. According to the method, the prediction precision of the complex river network under extreme conditions can be remarkably improved, the prediction result is ensured to accord with the law of conservation of momentum and quality, and the method has relatively high robustness and physical interpretability.

The application discloses a kind of based on deep learning's full-waveband microwave radiation transmission simulation method and system, method includes: based on global reanalysis data and surface type product, obtain atmospheric profile and surface parameter, adopt near neighbor search and de-redundancy, construct representative "surface parameter-atmospheric profile" database;Using high-precision microwave radiation transmission mode, simulate and calculate the atmospheric top layer brightness temperature covering full-waveband microwave, construct training sample pair;Calculate the correlation coefficient between all output channels, and select the representative channel subset with reduced number from threshold value;Build a fully connected neural network, with the brightness temperature of the representative channel subset as the intermediate feature layer, and use a phased composite loss function strategy for training;Surface parameters and atmospheric profile are input into the trained model to obtain full-waveband brightness temperature prediction results, and / or using automatic differentiation mechanism, the trained model is used as a differentiable operator to calculate the Jacobian matrix of the output brightness temperature relative to the input parameters.

The invention discloses a catastrophe prediction and risk assessment method for a defective road-stratum system based on a mechanical-data dual-drive model. The method relates to the technical field of road-stratum system catastrophe prediction and risk assessment. Comprising the steps that road collapse statistical data and engineering settlement measured data are collected, and a data set is constructed through preprocessing; a mechanical analysis model is established, road internal force and deflection are calculated based on a viscoelastic foundation beam theory, a Merchant rheological model and a modified Cambridge model are fused to solve stratum stress and cavity evolution, and a cooperative response control differential equation and boundary conditions are formed; a physical information neural network is constructed, a mechanical loss function is set, and a catastrophe agent model is obtained through automatic differential training; training an optimization network by using the data set to obtain a mechanical-data dual-drive prediction agent model; and introducing disaster-causing factor probability characteristics, and quantifying disaster probabilities under different defect conditions through probability simulation and risk assessment.

The invention discloses a truss structure nonlinear buckling stability optimization design method based on a finite mass point method and automatic differentiation, and the method comprises the steps: constructing a parameterized truss model, and taking the cross-sectional area and / or node coordinates of a rod piece in the parameterized truss model as design variables; constructing an optimization objective function for determining the nonlinear buckling stability performance of the structure as an objective; and on the basis of the parameterized truss model, constructing a corresponding finite mass point method analysis model, and performing iterative optimization on the optimization objective function in the process of simulating nonlinear static response to buckling in the finite mass point method analysis model in combination with automatic differential software, so as to output a final design variable as the optimal truss structure design. The method provided by the invention can effectively solve the problem of buckling stability optimization of the truss structure which becomes abnormally complex due to geometric nonlinearity and path dependence characteristics.

The invention relates to the technical field of aerospace and artificial intelligence, and provides a space target orbit intelligent prediction method fusing orbit dynamics constraints, which comprises the following steps: preprocessing original orbit data of a space target to generate a continuous complete time sequence data set with uniform time intervals; constructing a physical information neural network model representing input and output in a time sequence data form, and performing differential calculation on an output sequence by using an automatic differential mechanism; designing and introducing a loss function of an adaptive weighting mechanism, wherein the loss function is used for loss items of a network module and a physical module in a dynamic balance training process; training the physical information neural network model; setting a data subset sampling rate, constructing a multi-scale data scene, and evaluating the performance of the physical information neural network model under different data scale conditions. According to the method, the modeling capability of the long-time orbit evolution process can be improved, and dynamic adjustment of various loss item weights is realized.

The application discloses a kind of energy storage system prediction methods based on physical information neural network, first, the operating target of energy storage system is combined with security constraint, and the augmented state model containing electricity, thermology and attenuation mechanism is established, and prediction target is constructed;Second, PINN prediction network is constructed, and physical residual is calculated using automatic differentiation, to form a joint loss function consisting of data consistency loss, physical constraint loss and boundary penalty term;Then, BMS / EMS operating data is collected within the preset time interval, and the optimal model is solved based on the joint loss to update the network parameters;Finally, the trained model is deployed in the online rolling prediction link, and the predicted future SOC, temperature and available charge and discharge power are output, which are used as the scheduling input of energy management system.The method of the present application reduces the dependence on complex and high-precision mechanism modeling while ensuring that the prediction results meet the physical laws, achieving an integrated design from data and physical constraints to energy storage prediction and scheduling support.

Systems and methods for using compiler transforms to transform a non-local function into a local function are disclosed. The systems and methods perform a dynamic inter-procedural analysis before performing reverse-mode automatic differentiation. The dynamic inter-procedural analysis is performed to determine a maximum set of computer program information. A non-local to local transformation is applied to the determined maximum set of computer program information, and each original instruction is mapped to an optic that is represented as an opaque closure in the transformed local function.

A method for full-field inversion of corrected Mohr-Coulomb constitutive parameters based on automatic differentiation of computational graphs is presented, relating to the field of numerical simulation in geotechnical engineering. This method constructs a smoothed, differentiable corrected Mohr-Coulomb computational graph. After inputting initial data of the soil and rock mass to be analyzed, a forward finite element simulation is performed to obtain the simulated displacement field. The loss function is calculated, and its change is checked to determine convergence. If convergence is not achieved, the gradient is automatically calculated via backpropagation, and the parameters are updated using the L-BFGS optimization algorithm, with TV regularization constraints used to maintain the smoothness of the parameter field. The forward finite element simulation is repeated, and this process is iterated until convergence is achieved. The inverted parameter field is then output. By utilizing automatic differentiation technology, the accurate gradient of the full-field parameters can be obtained with a single backpropagation, introducing the automatic differentiation technology of deep learning frameworks into the field of geotechnical engineering, realizing the transformation from manual gradient derivation to automatic machine differentiation.

The application discloses a dimension reduction modeling method and device for ammonia synthesis reaction-heat transfer coupling process, comprising: constructing a forward propagation fully connected neural network with time coordinate t and axial space coordinate z as input; in the forward propagation process of the fully connected neural network, the mechanism expression of the ammonia synthesis reaction rate is explicitly embedded as a structural prior; based on the output of the fully connected neural network, the time and space derivatives of the ammonia mass fraction and the gas temperature are calculated through automatic differentiation, and a trend type penalty term loss, a mass conservation PDE residual loss, an energy conservation PDE residual loss and a boundary residual loss are constructed; the trend type penalty term loss is used to constrain the monotone increasing trend of the ammonia mass fraction and the temperature along the axial direction of the bed, and the penalty is generated only when the spatial derivative is negative; the total loss function is composed of the loss terms by weighting according to the preset weight, and the network parameters are optimized through back propagation, so that the dimension reduction solution and fast prediction of the reaction-heat transfer coupling partial differential equation are realized.

The application discloses a heat flow system partial differential equation group fast solving method based on a PINN algorithm, relates to the technical field of heat flow system simulation and simulation, and has the technical scheme as follows: a PINN model containing physical information of a heat flow system is constructed, heat flow system partial differential equation groups and boundary conditions and initial conditions thereof are embedded into a loss function of a neural network, a neural network architecture of heat flow system information is selected, the derivative of the partial differential equation groups is calculated by using automatic differentiation technology, the loss function is constructed, the parameters of the neural network are trained by using an optimization algorithm, the approximate solution of the partial differential equation groups is obtained, and the PINN model after training is verified and optimized. In the application, the automatic differentiation capability of the neural network is used to directly approximate the solution of the partial differential equation, the calculation complexity is significantly reduced, the traditional numerical method is avoided to depend on grid division, the dimension disaster problem in a high-dimensional problem is avoided, and an efficient and accurate tool is provided for the design, optimization and safety analysis of a nuclear reactor.

Provided herein are systems and methods comprising one or more virtual machines and a compiler to enable automatic differentiation across a stack. Further provided herein are technologies, integrations, and workflows to allow for automatic differentiation.

This disclosure relates to training and fine-tuning of neural networks on a neural processing unit. A core on a neural processing unit can perform matrix multiplication (MatMul) on tensors of different dimensions. A neural network can be trained through forward and backward operations, both of which can be offloaded to the core. For the forward operation, the core can perform a layer by performing MatMul on an input tensor and a weight tensor and generate an output tensor. A loss can be computed. For the backward operation, the core can compute a weight gradient of the loss by performing MatMul on a gradient of the output tensor and the input tensor, and compute an input gradient of the loss by performing MatMul on the gradient of the output tensor and the weight tensor. The gradient of the output tensor can be computed by an automatic differentiation module. The weight tensor can be updated based on the input gradient and the weight gradient.

The application discloses a cell migration behavior prediction method based on physical information width learning, which utilizes cell scratch experiment data to construct a base function matrix, combines a Fisher-KPP reaction diffusion equation to construct a nonlinear least square problem containing physical mechanism constraints, and adopts an enhanced nonlinear least square disturbance algorithm to iteratively solve output weights, so as to realize prediction of cell density space-time evolution. The application converts traditional deep network iterative training into a nonlinear least square problem, greatly reduces a search space through physical information initialization and linearization approximation, and realizes order-of-magnitude improvement of training speed. The application constructs a width learning architecture containing feature nodes and enhanced nodes, effectively avoids the gradient vanishing problem in deep learning, combines analytical derivative calculation, eliminates cumulative error of automatic differentiation on high-order derivatives, and can more accurately capture space-time evolution characteristics in cell migration.

The invention discloses a generalized Hamilton symplectic neural network dynamic response analysis method for an engineering structure. A sinchinger propagation operator is embedded in forward propagation of a neural network, so that the geometric structure and energy consistency of the system is kept; on this basis, a conservative dissipative double-branch network structure is constructed, a conservative branch keeps a track by using a symplectic propagation generation structure, and a dissipative branch independently depicts damping and external load effects, so that unified modeling of conservative and non-conservative systems is realized. An equation residual error and an energy regular term are constructed through an automatic differential technology, and unsupervised training can be realized without real trajectory data. According to the method, a coupling interface of a finite element generalized Hamilton neural network is established, mass, damping, stiffness matrixes and load vectors obtained through finite element analysis are mapped into a generalized Hamilton form, and high-precision dynamic response prediction of complex engineering structures such as stiffened wallboards is achieved.

The invention relates to a transient dynamic response calculation method and system for a high-dimensional complex nonlinear rotor system, and the method is characterized in that the method comprises the following steps: 1, obtaining a nonlinear dynamic equation of the rotor system, and carrying out the discretization of the nonlinear dynamic equation; 2, acquiring an algebraic equation which takes displacement response of a rotor system at a to-be-solved moment as a unique unknown quantity by utilizing two basic assumptions of a Newmak method, acquiring an accurate jacobian matrix J of the algebraic equation by utilizing an automatic differential function jacrev in PyTorch, and constructing a Newton-Raphson iterative format to perform iterative calculation; step 3, utilizing two basic assumptions of the Newmak method to further obtain the acceleration and the speed response of the rotor system at the moment to be solved; and step 4, repeating the step 2 to the step 3 to obtain the dynamic response of the rotor system at each moment until the set time is reached, and completing the calculation. According to the method, the problems of low efficiency and difficult solution of obtaining the transient dynamic response of the high-dimensional complex nonlinear rotor system at present are solved, the method can be widely applied to calculation of the transient dynamic response of the high-dimensional complex nonlinear rotor system, and the method has the characteristics of universality and modularization.

The application relates to the technical field of aerospace and artificial intelligence, and provides a space target orbit intelligent prediction method fusing an orbit dynamics constraint, which comprises the following steps: preprocessing original orbit data of a space target to generate a complete time series data set with continuity and uniform time intervals; constructing a physical information neural network model which represents input and output in the form of time series data, and performing differential calculation on an output sequence by using an automatic differentiation mechanism; designing and introducing a loss function with an adaptive weighting mechanism to dynamically balance loss terms of network modules and physical modules in a training process; training the physical information neural network model; setting a data subset sampling rate, constructing a multi-scale data scene, and evaluating performance of the physical information neural network model under different data scale conditions. The application can improve modeling capability for a long-time orbit evolution process and realize dynamic adjustment of weights of various loss terms.

The invention relates to the technical field of power grid planning, in particular to a high-performance parallel automatic differential method, system, equipment and medium for main distribution micro power flow nonlinear optimization, and by adopting the method provided by the invention, modeling is carried out based on a main distribution micro power flow nonlinear optimization problem, and an expression diagram is constructed; considering that a large number of isomorphic constraints exist in the problem, the constructed expression graphs are subjected to grouping management, and an automatic differential calculation function pointer used for calculating each group of instances is generated for a plurality of obtained expression groups. And finally, based on the constructed automatic differential calculation function pointer, introducing an OpenMP parallel framework, and carrying out automatic differential parallel calculation on each expression group. Based on the experimental result of opfbenchmark, the method provided by the invention improves the calculation efficiency of automatic differentiation by 47% in the main distribution micro nonlinear optimization problem.