Neural network modeling method and apparatus for non-adiabatic time-dependent density functional dynamics

Abstract

This application provides a neural network modeling method and apparatus for nonadiabatic time-dependent density functional dynamics, relating to the technical field of interdisciplinary artificial intelligence and computational physics. The method includes: constructing a phase space state vector based on the real and imaginary parts of the complex state coefficients of the occupied orbits to obtain a feature representation; inputting the feature representation into a Hamiltonian dynamics branch to obtain a Hamiltonian-induced vector field; inputting the feature representation into a direct vector field branch to obtain a direct vector field; and inputting the feature representation into a memory exchange-correlation potential branch to obtain an exchange-correlation potential. The method and apparatus provided in this application, by constructing a three-headed neural network including a Hamiltonian dynamics branch, a direct vector field branch, and a memory exchange-correlation potential branch, simultaneously model the structure, residuals, and memory. This achieves higher accuracy, better long-term stability, and stronger physical interpretability compared to existing technologies in simulating strongly nonequilibrium, long-term nonadiabatic dynamic processes.

Description

Technical Field

[0001] This application relates to the technical field of the intersection of artificial intelligence and computational physics, and in particular to a neural network modeling method and apparatus for nonadiabatic time-dependent density functional dynamics. Background Technology

[0002] Time-dependent density functional theory (TDDFT) is an important method for studying the nonequilibrium quantum dynamics of electronic systems. Its computational accuracy and engineering usability largely depend on the approximate quality of the exchange-correlation potential. Strictly speaking, the exchange-correlation potential is a causal functional about the entire history of electron density and is related to the initial state of the interacting system and the Kohn-Sham initial state. Its exact analytical form is unknown, so practical calculations generally rely on approximate exchange-correlation functionals.

[0003] Related techniques employ adiabatic approximations, such as the Adiabatic Local Density Approximation (ALDA) and the Generalized Gradient Approximation (GGA). These methods typically apply the ground-state exchange-correlation functional directly to the instantaneous density, thus neglecting the dependence of the exchange-correlation potential on historical density and initial-state information. While these approximations are relatively robust under weak perturbations, slowly varying, and near-linear responses, they often fail to accurately describe the time-local behavior of real systems in strongly nonequilibrium, rapidly evolving, and memory-effect-prominent nonadiabatic dynamic processes, leading to accumulated propagation errors and biased dynamic predictions. Particularly in ultrafast processes with strong electron-nuclear coupling, nonadiabatic scattering processes, and complex systems with significant energy dissipation, neglecting memory effects directly impacts the accuracy of exchange-correlation potential modeling and the final dynamic simulation results.

[0004] Furthermore, while some existing data-driven methods attempt to use neural networks to learn and model dynamic processes or exchange-related potentials, they often struggle to simultaneously consider physical structural constraints, time memory representations, and long-term propagation stability. Therefore, they still cannot meet the needs of complex non-adiabatic time-dependent density functional dynamics modeling. Summary of the Invention

[0005] This application provides a neural network modeling method and apparatus for non-adiabatic time-dependent density functional dynamics, which addresses the current technical problem of the urgent need for a unified modeling method and implementation path that can simultaneously take into account physical structure consistency, data-driven correction capability and time memory modeling capability, and ensure long-term propagation stability.

[0006] This application provides a neural network modeling method for non-adiabatic time-dependent density functional dynamics, including: A phase space state vector is constructed based on the real and imaginary parts of the complex state coefficients of the occupied orbit, and a feature representation is obtained through an embedding layer. The feature representation is input into the Hamiltonian dynamics branch of the three-head neural network to obtain the Hamiltonian induced vector field. The feature representation is input into the direct vector field branch of the three-head neural network to obtain the direct vector field representing the data-driven correction. The feature representation is input into the memory exchange correlation potential branch of the three-head neural network, and the historical information is encoded using a recurrent neural network to obtain the exchange correlation potential. The exchange correlation potential is then normalized. The Hamiltonian dynamics branch and the direct vector field branch are coupled through a two-way information exchange mechanism, and each branch maintains long-term modeling continuity through a cross-time window state transfer mechanism; the three-head neural network is jointly trained based on dynamic supervision loss and exchange correlation potential supervision loss.

[0007] In some embodiments, the Hamiltonian dynamics branch and the direct vector field branch exchange information bidirectionally based on nested outer loop iterations and inner loop iterations: In each outer loop iteration, an inner loop iteration is performed a preset number of times, where the preset number of times is at least once; In each inner loop iteration, the current hidden state of the Hamiltonian dynamics branch is combined with the feature representation to generate a guidance signal, and the hidden state of the direct vector field branch is updated based on the guidance signal. After completing the preset number of inner loop iterations, the hidden state of the Hamiltonian dynamics branch is updated based on the updated hidden state of the direct vector field branch.

[0008] In some embodiments, inputting the feature representation into the Hamiltonian dynamics branch of a three-headed neural network to obtain a Hamiltonian induced vector field includes: The feature representation is input into the Hamiltonian dynamics branch, which then performs the following steps: The feature representation is processed based on a feedforward neural network to obtain a scalar Hamiltonian. The scalar Hamiltonian is differentiated, and the result of the differentiation is combined with the standard symplectic matrix to obtain the Hamiltonian induced vector field.

[0009] In some embodiments, the step of inputting the feature representation into the direct vector field branch of a three-headed neural network to obtain a direct vector field characterizing the data-driven correction includes: The feature representation is input into the direct vector field branch, and the direct vector field branch performs the following steps: The hidden representation is obtained by mapping the feature representation based on the backbone network. The hidden representation is projected onto the first linear mapping layer to output a direct vector field representing the time derivative.

[0010] In some embodiments, the step of inputting the feature representation into the memory exchange-correlation potential branch of a three-headed neural network, encoding historical information using a recurrent neural network to obtain the exchange-correlation potential, and performing normalization processing on the exchange-correlation potential includes: The feature representation is input into the memory exchange correlation potential branch, and the memory exchange correlation potential branch performs the following steps: The feature representations are processed along the time axis using a recurrent neural network to obtain a sequence of hidden states; The hidden state sequence is mapped to a grid-resolved exchange correlation potential based on the second linear projection layer; The exchange correlation potential is normalized to zero mean.

[0011] In some embodiments, the method further includes: The time series represented by the features is divided into multiple consecutive time windows along the time axis; After completing the processing of the current time window, the updated hidden states of the Hamiltonian dynamics branch and the direct vector field branch corresponding to the current time window are compressed along the batch processing dimension to obtain the carrying state of each branch. Perform a computation graph separation operation on the carried state to truncate the gradients backpropagating from subsequent time windows to the current time window; The carried state after separation by computational graph is used as the initial state of the next time window, and after being copied along the batch processing dimension, it is used to initialize the hidden state of the Hamiltonian dynamics branch and the direct vector field branch in the next time window.

[0012] In some embodiments, the method further includes: Based on the loss of the Hamiltonian dynamics branch, the loss of the direct vector field branch, and the consistency constraint loss between the Hamiltonian dynamics branch and the direct vector field branch, the dynamics supervision loss is determined. The loss function of the three-head neural network is determined based on the dynamic supervision loss and the exchange correlation potential supervision loss of the memory exchange correlation potential branch.

[0013] This application provides a neural network modeling device for non-adiabatic time-dependent density functional dynamics, comprising: The phase space representation and input embedding module is used to construct a phase space state vector based on the real and imaginary parts of the complex state coefficients of the occupied orbit, and obtain feature representations through the embedding layer. The Hamiltonian dynamics modeling module is used to input the feature representation into the Hamiltonian dynamics branch of the three-head neural network to obtain the Hamiltonian induced vector field. The direct vector field modeling module is used to input the feature representation into the direct vector field branch of the three-head neural network to obtain a direct vector field representing the data-driven correction. The memory exchange correlation potential modeling module is used to input the feature representation into the memory exchange correlation potential branch of the three-head neural network, encode historical information using a recurrent neural network to obtain the exchange correlation potential, and perform normalization processing on the exchange correlation potential. The Hamiltonian dynamics branch and the direct vector field branch are coupled through a two-way information exchange mechanism, and each branch maintains long-term modeling continuity through a cross-time window state transfer mechanism; the three-head neural network is jointly trained based on dynamic supervision loss and exchange correlation potential supervision loss.

[0014] This application provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the neural network modeling method for non-adiabatic time-dependent density functional dynamics.

[0015] This application provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the neural network modeling method for non-adiabatic time-dependent density functional dynamics.

[0016] The neural network modeling method and apparatus for nonadiabatic time-dependent density functional dynamics provided in this application realize a novel modeling paradigm for nonadiabatic quantum dynamics problems by constructing a three-headed neural network architecture including a Hamiltonian dynamics branch, a direct vector field branch, and a memory exchange-correlated potential branch. Among them, the memory exchange-correlated potential branch explicitly introduces the time memory effect using a recurrent neural network structure, solving the fundamental defects of the adiabatic approximation. The parallel setting of the Hamiltonian dynamics branch and the direct vector field branch, as well as the bidirectional information exchange mechanism between them, cleverly balances the relationship between the strict preservation of physical laws (structural consistency) and the data-driven correction of complex realities (accuracy and robustness). This integrated design enables the model to simultaneously model the structure, residuals, and memory within a unified framework, thereby achieving higher accuracy, better long-term stability, and stronger physical interpretability compared to existing technologies in simulating strongly nonequilibrium, long-term nonadiabatic dynamic processes. Attached Figure Description

[0017] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0018] To more clearly illustrate the technical solutions in this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a flowchart illustrating the neural network modeling method for non-adiabatic time-dependent density functional dynamics provided in this application.

[0020] Figure 2 This is the architecture diagram of the three-head neural network provided in this application.

[0021] Figure 3 This is a schematic diagram of the neural network modeling device for non-adiabatic time-dependent density functional dynamics provided in this application.

[0022] Figure 4 This is a schematic diagram of the structure of the electronic device provided in this application. Detailed Implementation

[0023] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present application.

[0024] It should be noted that the terms "first," "second," etc., used in this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or device that comprises a series of steps, units, or modules is not necessarily limited to those explicitly listed, but may include other steps, units, or modules not explicitly listed or inherent to such processes, methods, products, or devices.

[0025] Existing research has shown that accurate time-varying exchange-correlation potentials typically exhibit significant time nonlocality, meaning they depend not only on the current electron density but also on the system's historical evolution and initial conditions. Therefore, common adiabatic approximation methods, which usually construct exchange-correlation potentials based only on instantaneous densities, are insufficient to fully characterize the aforementioned time-memory effects.

[0026] To overcome the limitations of adiabatic approximation methods, several non-adiabatic improvement paths have been proposed: one type introduces frequency-dependent exchange-correlation kernels within the frequency domain framework, primarily serving linear response frameworks; another type employs generalized forms such as time-dependent current density functional theory with current density as the fundamental variable, theoretically improving the local approximation of dynamic responses. However, these traditional non-adiabatic methods typically have strong applicability constraints, often involving more physical quantities, additional approximation constructions, and more complex computational processes in practical numerical implementations. Therefore, in strongly nonlinear, strongly nonequilibrium, and long-time-propagation scenarios, they still face problems such as high implementation complexity, limited applicability, and insufficient scalability. Based on this, related research further explores the use of data-driven methods to model non-adiabatic dynamics.

[0027] Data-driven approaches refer to directly using machine learning to learn exchange-related potentials from dynamic data, aiming to reproduce non-adiabatic structures and improve propagation accuracy in specific systems. Although there are already many data-driven methods in related technologies, there are still some common shortcomings and unresolved issues in non-adiabatic dynamic modeling for strong nonequilibrium and long-term propagation.

[0028] First, the most commonly used adiabatic exchange-dependent potential approximations (such as the adiabatic local density approximation and the generalized gradient approximation) are simple and stable in implementation, but their basic assumption is that they depend only on instantaneous density and ignore historical dependence. For cases with weak perturbations and slow changes, and near-linear responses, this approach can usually give acceptable results; however, in fast nonequilibrium dynamics, the influence of historical dependence on force and flow is amplified, thereby affecting the reliability of the propagation process and the final physical quantities.

[0029] Secondly, in traditional improvement approaches for non-adiabatic effects, methods such as frequency-dependent exchange-correlation kernels and time-dependent current density functional theory hold a clear theoretical position in the analysis of dynamic linear responses and provide a systematic framework for characterizing dynamic responses. However, in practical numerical applications, these methods often serve linear responses or specific frequency settings more naturally, and their engineering implementation involves additional physical quantities and approximation selections, making the overall implementation relatively complex.

[0030] Third, recent data-driven work has jointly promoted the development of learning-based TDDFT, but it has also exposed several common challenges, such as how to effectively represent and learn the temporal memory information in the exchange-related potential, and how to maintain the structural consistency, numerical stability, and physical rationality of model predictions over longer propagation timescales. In particular, some existing data-driven methods focus more on the fitting ability itself in model design, and still lack sufficient consideration for the synergistic relationship between physical structural constraints, temporal memory modeling, and long-term propagation stability.

[0031] In summary, although relevant technologies have developed usable solutions within their respective problem domains, there is still a lack of a unified modeling and implementation path that can simultaneously take into account structural consistency, data-driven correction, and explicit time memory, and adapt to long-term propagation requirements for learning modeling tasks of non-adiabatic time-dependent density functional dynamics.

[0032] In order to address the shortcomings of related technologies, Figure 1 This is a flowchart illustrating the neural network modeling method for non-adiabatic time-dependent density functional dynamics provided in this application, as shown below. Figure 1 As shown, the method includes steps 110, 120, 130, and 140. Steps 120 to 140 can be performed in parallel.

[0033] Step 110: Construct a phase space state vector based on the real and imaginary parts of the complex state coefficients of the occupied orbit, and obtain a feature representation through an embedding layer.

[0034] Specifically, the execution entity of the neural network modeling method for non-adiabatic time-dependent density functional dynamics provided in this application embodiment is a neural network modeling system. This system can be implemented in software, such as a neural network modeling program for non-adiabatic time-dependent density functional dynamics; or it can be a device for executing the neural network modeling method for non-adiabatic time-dependent density functional dynamics, such as a terminal, computer, or server.

[0035] Interacting multi-electron systems are objects of study in quantum chemistry and condensed matter physics, such as molecules, atomic clusters, or periodic solid materials. These systems undergo dynamic evolution under the influence of external fields (such as laser pulses).

[0036] Occupied orbits typically refer to time-dependent Kohn-Sham (KS) orbits, denoted as ,in For track indexing, For spatial coordinates, For time. Time-dependent Kohn–Sham orbitals are auxiliary single-particle orbitals in time-dependent density functional theory, used to characterize the time evolution of the electron density of the system.

[0037] A time series refers to a series of snapshots of the orbital changes over time during dynamic evolution. These data can be obtained indirectly through more precise theoretical calculations (as a reference benchmark) or experimental measurements.

[0038] Determining the characteristic representation used to characterize the phase space state involves preprocessing and transforming the original orbital wavefunction, expressed in spatial coordinates, to obtain a numerical representation suitable for the input of a neural network model. This step serves as a bridge connecting the physical world and machine learning models.

[0039] In a specific implementation example, this step may include: First, for each occupied orbit Complex state coefficients in discrete space representation The complex state coefficients are extracted, and can be derived from either the grid discretization representation or the basis set expansion representation. This step discretizes the continuous function into a set of coefficient vectors.

[0040] Then, the resulting complex state coefficient vector It is decomposed into real and imaginary parts, that is... ,in , .

[0041] Next, the real part of each orbital... and the virtual part Stacked together, they form a real vector. In Hamiltonian mechanics, this is equivalent to mapping the system from complex Hilbert space to real space, where... and These can be considered as generalized coordinates and generalized momentum, respectively. Therefore, It can be referred to as the phase space state vector of an orbit.

[0042] Finally, all of the system The phase space state vector of each occupied orbit The vectors are concatenated to form a higher-dimensional global state vector. The vector at a certain moment The value of This fully describes the quantum state of the entire electronic system at that moment.

[0043] During training and inference, The time series is organized into input tensors by window. ,in For batch size, For window length, Let be the dimension of the phase space. The input vector at each time step. Input embedding can be performed (this can be achieved through embedding layers in a neural network). Indicates the sample number in the batch. The time step number within the window is used to obtain the feature representation used to characterize the phase space state. This feature is then used as a shared representation entry point for the three-headed neural network.

[0044] Through this step, the original, complex orbital data in functional form is transformed into a real-number feature representation with a uniform format and fixed dimensions, which can be directly used as input to the subsequent three-head neural network.

[0045] The three-head neural network receives the generated feature representations as shared inputs and feeds them in parallel into three branches (or "heads") with different functions and structures for processing. These three branches are: Hamiltonian Dynamics (HD-Head), Direct Vector Field (DVF-Head), and Memory Exchange Correlated Potential (MXC-Head). This multi-task, multi-branch architecture aims to decompose complex dynamical evolution problems into several interconnected but distinct sub-tasks.

[0046] Step 120: Input the feature representation into the Hamiltonian dynamics branch of the three-headed neural network to obtain the Hamiltonian induced vector field.

[0047] Specifically, the Hamiltonian dynamics branch is a neural network module designed to learn the parts of a dynamic system that conform to the physical structure. It aims to learn the Hamiltonian of the system and thereby derive the dynamic evolution direction that satisfies the fundamental principles of Hamiltonian mechanics (i.e., symplectic structure).

[0048] Hamiltonian induced vector fields are used to characterize the phase space state-time derivatives constrained by Hamiltonian structures. Since the dynamic output of this branch is explicitly generated by scalar Hamiltonians and fixed symplectic transforms, symplectic geometric constraints can be embedded in the network, providing physically inspired structured priors for the model and improving the stability and physical consistency of long-term dynamic propagation.

[0049] Step 130: Input the feature representation into the direct vector field branch of the three-head neural network to obtain the direct vector field with data-driven correction.

[0050] Specifically, the direct vector field branch is another parallel neural network module. Its design goal is to learn the time derivatives of the system state directly from the data, as a supplement and correction to the Hamiltonian dynamics branch.

[0051] The direct vector field is a vector output directly from this branch. It aims to capture complex dynamic effects that are difficult to describe by a pure Hamiltonian structure, such as errors introduced by numerical discretization, weak coupling between the system and the environment, or residual components such as non-ideal non-Hamiltonian forces. This branch provides the model with high flexibility and data fitting capabilities.

[0052] To ensure that the Hamiltonian dynamics branch (physical structure branch) and the direct vector field branch (data correction branch) can work together, rather than simply output in parallel, a nested two-way information exchange mechanism is set up to ensure that information is passed on to each other and influences each other during the calculation of these two branches.

[0053] In a single time step of computation, the more physically structured information generated by the Hamiltonian dynamics branch (such as its internal hidden states or preliminary predictions) can be used as a guiding signal to constrain or guide the learning of the direct vector field branch, preventing it from deviating from its physical trajectory. Conversely, the residual correction information learned by the direct vector field branch from the data can also be fed back to the Hamiltonian dynamics branch, helping it adjust its overall perception of the system state, thereby producing a more accurate Hamiltonian. This bidirectional coupling mechanism allows the two parts of the model to continuously align and calibrate each other during training. Specifically, this information exchange can be achieved by establishing connections between the hidden layers of the two branches and fusing information through iterative updates, ensuring that the final output is the result of their collaborative action.

[0054] Step 140: Input the feature representation into the memory exchange correlation potential branch of the three-head neural network, encode the historical information using a recurrent neural network to obtain the exchange correlation potential, and perform normalization processing on the exchange correlation potential.

[0055] Specifically, the memory exchange-related potential branch is the third parallel neural network module. Its core task is to address a key deficiency in existing adiabatic approximations, namely, neglecting the memory effect. It aims to learn an exchange-related potential that explicitly depends on the system's historical states.

[0056] The exchange-correlation potential is a core physical quantity in density functional theory, encompassing all nontrivial many-body interaction effects. This branch outputs a predicted exchange-correlation potential defined on a real-space grid to characterize the spatial and temporal variation structure of the exchange-correlation potential.

[0057] To model the memory, the memory exchange-correlation potential branch employs a recurrent neural network (RNN) structure along the time axis. This means that when processing time series data, the hidden state of this branch at the current time step depends not only on the input at the current moment but also on the hidden state passed from the previous time step. This cyclically dependent structure allows the network's output (i.e., the exchange-correlation potential) to explicitly depend on the system state information at all past moments, thereby effectively encoding historical information or memory effects in non-adiabatic dynamics.

[0058] The recurrent neural network structures in the embodiments of this application include, but are not limited to, Long Short-Term Memory (LSTM) networks, gated recurrent units, etc. These structures, through sophisticated gating mechanisms, can more effectively learn and maintain long-term temporal dependencies.

[0059] In this embodiment, the output exchange-correlation potential is also normalized by applying a zero-mean gauge. Since the exchange-correlation potential itself has a constant-shifted degree of freedom in its gauge, direct fitting may result in a non-unique objective. Introducing zero-mean normalization fixes the degree of freedom, ensuring the learning objective is unique at each time step, thereby improving the model's identifiability and stabilizing the optimization process.

[0060] In the embodiments of this application, the Hamiltonian dynamics branch and the direct vector field branch are coupled through a two-way information exchange mechanism, and each branch maintains the continuity of long-term modeling through a cross-time window state transfer mechanism.

[0061] Specifically, to achieve a deep integration of physical constraints and data-driven approaches, embodiments of this application design a bidirectional information interaction mechanism between the Hamiltonian dynamics branch and the direct vector field branch. For example, a hierarchical inference architecture can be adopted, where nested loops allow the energy state of higher layers to guide the update of the vector field in lower layers, and the latest state of the lower layers is then fed back to update the state of the higher layers. This enables the physical skeleton and the residual correction channel to continuously coordinate and align during inference and training.

[0062] Meanwhile, for long sequence data, this application employs a cross-window carry mechanism for state transfer. After processing one time window, the hidden states (including cell states in recurrent neural networks) are processed along the batch dimension (e.g., average compression) and the backpropagation of the computation graph is truncated, serving as the initial state for the next window. This mechanism preserves long-range contextual information across windows with controlled memory overhead, effectively avoiding gradient explosion and improving the numerical stability of training.

[0063] During the joint training phase, the model's total loss function consists of several parts: first, a dynamic supervision loss calculated for the derivatives of the Hamiltonian induced vector field and the direct vector field with respect to the true reference; second, a consistency constraint loss introduced between the Hamiltonian branch and the direct vector field branch, ensuring mutual traction and preventing unconstrained drift of the data-driven branch; and third, a supervision loss calculated for the normalized exchange correlation potential of the memory branch output. This multi-objective joint optimization guides the model to achieve an optimal balance between physical interpretability and numerical prediction accuracy.

[0064] The neural network modeling method for nonadiabatic time-dependent density functional dynamics provided in this application realizes a novel modeling paradigm for nonadiabatic quantum dynamics problems by constructing a three-headed neural network architecture that includes a Hamiltonian dynamics branch, a direct vector field branch, and a memory exchange-related potential branch. The memory exchange-related potential branch explicitly introduces a time memory effect using a recurrent neural network structure, solving the fundamental defects of the adiabatic approximation. The parallel setup of the Hamiltonian dynamics branch and the direct vector field branch, and the bidirectional information exchange mechanism between them, cleverly balance the relationship between the strict preservation of physical laws (structural consistency) and data-driven corrections for complex realities (accuracy and robustness). This integrated design enables the model to simultaneously model the structure, residuals, and memory within a unified framework, thereby achieving higher accuracy, better long-term stability, and stronger physical interpretability compared to existing technologies in simulating strongly nonequilibrium, long-term nonadiabatic dynamics.

[0065] It should be noted that each implementation method of this application can be freely combined, rearranged, or executed individually, and does not need to rely on or depend on a fixed execution order.

[0066] In some embodiments, the Hamiltonian dynamics branch and the direct vector field branch exchange information bidirectionally based on nested outer loop iterations and inner loop iterations: In each outer loop iteration, the inner loop iteration is performed a preset number of times, with the preset number being at least once; In each inner loop iteration, the current hidden state of the Hamiltonian dynamics branch is combined with the feature representation to generate a guidance signal, and the hidden state of the direct vector field branch is updated based on the guidance signal. After completing a preset number of inner loop iterations, the hidden state of the Hamiltonian dynamics branch is updated based on the updated hidden state of the direct vector field branch.

[0067] Specifically, during the processing of a time step, the hidden state updates of the two branches are not completed at once, but are performed iteratively through a nested loop.

[0068] The outer loop iteration is an update process performed on the hidden states of the Hamiltonian dynamics branch. This update process is iterative. Second-rate, This can be a preset integer hyperparameter. In each outer loop iteration, the hidden state of the Hamiltonian dynamics branch is updated based on the information from the direct vector field branch feedback.

[0069] The inner loop iteration is the update process for the hidden state of the direct vector field branch. It is nested within each iteration of the outer loop. In the current outer loop iteration, the inner loop iterations are executed a preset number of times. The preset number is at least one. For example, the inner loop can iterate... Second-rate, This can be a preset integer hyperparameter. The direct vector field branch will be updated before the Hamiltonian dynamics branch is updated. This is a more refined internal adjustment.

[0070] The current hidden state of the Hamiltonian dynamics branch refers to the state at the 1st... At the start of the next outer loop, the internal state vector maintained by this branch is denoted as... The current hidden state and feature representation of the Hamiltonian dynamics branch can be combined in various ways, such as vector concatenation, element-wise addition, or fusion through a small neural network. In a specific embodiment, the combination method is vector addition, i.e., the guiding signal is... This guidance signal integrates high-level information from the physical structure branches and instantaneous information from the current input.

[0071] The direct vector field branch receives this guidance signal and combines it with its own hidden state from the previous inner loop iteration. Through its own update function To calculate and update its hidden state to This process can be represented as: .

[0072] when After all inner loops are completed, the hidden state of the direct vector field branch. The guidance signal has been fully absorbed and self-adjusted. At this point, this finely refined hidden state, more closely aligned with the data details, will be used to update the Hamiltonian dynamics branch. Specifically, the Hamiltonian dynamics branch will receive this feedback signal. And combine it with its own hidden state at the start of the current outer loop iteration. Through its own update function This completes the update of the outer loop and yields a new hidden state. This process can be represented as: .

[0073] Through the nested, iterative update process described above, the bidirectional information exchange described in the embodiments of this application is realized.

[0074] The neural network modeling method for non-adiabatic time-dependent density functional dynamics provided in this application embodiment, based on a nested loop update mechanism, enables more thorough and in-depth information fusion between the two branches; it ensures that the physical structure of the Hamiltonian branch can effectively transfer and constrain the direct vector field branch, preventing it from generating physically meaningless drift when fitting data; at the same time, it also ensures that the fine correction information learned by the direct vector field branch from the data can be effectively absorbed by the Hamiltonian branch.

[0075] In some embodiments, the feature representation is input into the Hamiltonian dynamics branch of a three-headed neural network to obtain a Hamiltonian induced vector field, including: The feature representation is input into the Hamiltonian dynamics branch, which then performs the following steps: The feature representation is processed based on a feedforward neural network to obtain a scalar Hamiltonian. The scalar Hamiltonian is differentiated, and the result is combined with the standard symplectic matrix to obtain the Hamiltonian induced vector field.

[0076] Specifically, after the feature representation is fed into the Hamiltonian dynamics branch, it is first processed by a feed-forward neural network (FNN).

[0077] A feedforward neural network can be a type of multi-layer perceptron (MLP). This network consists of one or more hidden layers, whose role is to learn a nonlinear mapping from the phase space state feature representation of the input to the total energy of the system.

[0078] To ensure the stability and physical meaning of subsequent differential calculations, the activation function of this feedforward neural network can preferably be a smooth function, such as the hyperbolic tangent function (tanh). Using a bounded and smooth activation function like tanh helps the network output a smooth and bounded potential energy surface, which is crucial for avoiding gradient explosion or vanishing problems in subsequent differentiation.

[0079] The final output of this feedforward neural network is a scalar Hamiltonian, denoted as . This is a single numerical value (scalar), not a vector.

[0080] After obtaining the scalar Hamiltonian Then, the dynamics were derived using the basic equations of Hamiltonian mechanics.

[0081] Differentiating the scalar Hamiltonian specifically refers to calculating the gradient of the Hamiltonian with respect to the characteristic representation of the phase space state, i.e. In modern deep learning frameworks (such as PyTorch, TensorFlow, etc.), this step can be completed efficiently and accurately using automatic differentiation (Auto-Diff) techniques.

[0082] Standard symplectic matrix, denoted as , is a fundamental structural matrix in Hamiltonian mechanics. This matrix is ​​fixed and reflects the geometric structure of Hamiltonian mechanics.

[0083] Combining the differential calculation result with the standard symplectic matrix specifically involves performing matrix-vector multiplication to obtain the Hamiltonian induced vector field. This can be expressed as a formula: .

[0084] This vector field gives the time derivative of the phase space state, i.e., the rate and direction of the system's evolution in phase space. Since it is derived from a scalar potential (Hamiltonian) through rigorous physical equations, it naturally satisfies symplectic geometry and remains end-to-end differentiable.

[0085] The neural network modeling method for non-adiabatic time-dependent density functional dynamics provided in this application combines the function fitting ability of neural networks (learning scalar Hamiltonians) with the first principles of physics (Hamiltonian canonical equations) to construct a Hamiltonian dynamics branch with intrinsic physical structure. This allows the model to learn complex dynamics while its output dynamic backbone naturally and structurally guarantees the symplectic structure of Hamiltonian mechanics. This greatly enhances the stability and accuracy of the model in long-term rolling predictions, effectively suppresses the error accumulation and structural drift problems common in traditional pure data-driven models, and makes reliable simulation of long-term dynamic evolution possible.

[0086] In some embodiments, the feature representation is input into the direct vector field branch of the three-head neural network to obtain a direct vector field characterizing the data-driven correction, including: The feature representation is input into the direct vector field branch, which then performs the following steps: The hidden representation is obtained by mapping the feature representation based on the backbone network; The hidden representation is projected based on the first linear mapping layer, and a direct vector field representing the time derivative is output.

[0087] Specifically, after the feature representation is fed into the direct vector field branch, it first goes through a backbone network for processing.

[0088] The backbone network can be implemented using feedforward neural networks, multilayer perceptrons, or other neural network structures suitable for feature extraction. The output of the backbone network is a hidden representation, which is used to characterize the abstract representation of the input state in the latent feature space, without necessarily maintaining a one-to-one correspondence with the original phase space coordinates.

[0089] After obtaining the hidden representation, this branch generates the final output through the first linear mapping layer.

[0090] The first linear mapping layer is a standard fully connected layer without a non-linear activation function. Its function is essentially a linear transformation, projecting the high-dimensional, abstract hidden representation back to the original phase space dimension.

[0091] The output of this linear layer is the direct vector field, which can be denoted as follows in this embodiment: It is used to characterize dynamic details and residual corrections that are not limited by structural form.

[0092] The neural network modeling method for non-adiabatic time-dependent density functional dynamics provided in this application effectively captures and models dynamic components that are difficult to describe or ignore by the Hamiltonian dynamics branch through the direct vector field branch. By combining this branch with the Hamiltonian dynamics branch, the details can be accurately corrected in a data-driven manner while maintaining the main physical structure, thereby significantly improving the prediction accuracy and robustness of the overall modeling scheme in complex, non-ideal, and strongly non-equilibrium scenarios.

[0093] In some embodiments, the feature representation is input into the memory exchange-correlation potential branch of a three-headed neural network, historical information is encoded using a recurrent neural network to obtain the exchange-correlation potential, and normalization processing is performed on the exchange-correlation potential, including: The feature representation is input into the memory exchange correlation potential branch, which then performs the following steps: The feature representations are processed along the time axis using a recurrent neural network to obtain a sequence of hidden states; The hidden state sequence is mapped to a grid-resolved exchange correlation potential based on the second linear projection layer; The exchange correlation potential is normalized to zero mean.

[0094] Specifically, after the feature representation is fed into the memory-exchange correlation potential branch at each time step, it is first processed by a recurrent neural network. Through this chain-like computational structure along the time axis, the hidden state at the current time step recursively contains the influence of all input information from the initial time step to the current time step. Therefore, the output of this recurrent neural network, namely the sequence of hidden states, naturally carries the historical information of the system's evolution, or what we might call memory. This is the structural basis for this branch's ability to model non-adiabatic effects.

[0095] In one specific embodiment, a Long Short-Term Memory (LSTM) network can be used as the specific implementation of a recurrent neural network.

[0096] After obtaining the hidden state sequence containing historical information, it needs to be transformed into a physically meaningful quantity, namely the exchange-correlation potential defined in real space. This step is accomplished through a second linear mapping layer.

[0097] The second linear mapping layer is a standard fully connected layer without a non-linear activation function. Its function is to transform the abstract sequence of hidden states (dimensions equal to the hidden state dimensions) output by the recurrent neural network into a vector with dimensions matching the number of grid points in the real space. The output of this linear layer is the exchange-correlation potential predicted in this application, denoted as... .

[0098] Furthermore, considering that the exchange-correlation potential is determined only in the sense of an additive constant at each time step, zero-mean normalization can be performed on the exchange-correlation potential to improve the identifiability of the learning objective and the stability of training. Specifically, at each time step, the predicted exchange-correlation potential on the spatial grid is subtracted from its spatial mean, thus obtaining the uniquely normalized representation of the exchange-correlation potential. This process reduces the impact of arbitrary constant shifts on the learning process.

[0099] The neural network modeling method for non-adiabatic time-dependent density functional dynamics provided in this application constructs an end-to-end mapping from dynamic history to instantaneous exchange-related potentials through a "recurrent neural network + linear projection layer" architecture. The recurrent neural network is responsible for memorizing and encoding historical information from the time series, while the linear projection layer is responsible for decoding this abstract memorized information into specific physical quantities. This directly solves the fundamental problem of existing adiabatic approximation methods ignoring historical dependence, enabling the model to capture and reproduce physical phenomena dominated by non-adiabatic effects.

[0100] In some embodiments, the method further includes: The time series represented by the features is divided into multiple successive time windows according to the time axis; After completing the processing of the current time window, the updated hidden states of the Hamiltonian dynamics branch and the direct vector field branch corresponding to the current time window are compressed along the batch processing dimension to obtain the carried state of each branch. Perform a computation graph separation operation on the carried state, truncating the gradients backpropagated from subsequent time windows to the current time window; The carried state after separation by computational graph is used as the initial state of the next time window, and after being copied along the batch processing dimension, it is used to initialize the hidden state of Hamiltonian dynamics branch and direct vector field branch in the next time window.

[0101] Specifically, before training or inference begins, the feature representation of the complete, very long time series is first divided along the time axis into multiple consecutive, non-overlapping subsequences of fixed (or variable) length. Each subsequence is a time window. In the training of neural networks, one or more such time windows are typically processed as a batch of data.

[0102] After inputting batch data consisting of one or more time windows into the model, the Hamiltonian dynamics branch and the direct vector field branch process the corresponding windows based on the shared backbone network, and obtain the updated hidden state trajectories within the window. The updated hidden states can be represented as window-level hidden state tensors.

[0103] After processing within the current time window, the updated hidden states corresponding to the Hamiltonian dynamics branch and the direct vector field branch are compressed along the batch processing dimension to generate the carrying state. Compression along the batch processing dimension involves performing a pooling operation on the final hidden states of this batch to obtain a single vector representing the average state of the entire batch. A specific compression operation is averaging, which involves summing the final hidden state vectors of all samples in the batch and dividing by the batch size.

[0104] After compression, the batch dimension of the resulting hidden state vectors is eliminated. This is the pair of compressed hidden state vectors. This refers to the carried state. It summarizes the average dynamic state information of the entire batch of samples at the end of the current time window.

[0105] The computation graph detachment operation, typically implemented in deep learning frameworks, is called the detach method. Performing this operation on a tensor creates a new tensor that shares data with the original tensor but does not carry gradient information. This means that during backpropagation to compute gradients, the gradient stream is truncated upon reaching this new tensor and cannot propagate further to the computation node that generated the original tensor.

[0106] Applying this operation to the carried state has the effect that when the model calculates the loss and performs backpropagation in subsequent time windows, the gradient will only propagate to the inside of the next window, and will not propagate back to the current window across the window boundary.

[0107] Although the states separated by the computational graph do not carry gradients, they still numerically contain the state information at the end of the previous window.

[0108] At the start of processing in the next time window, this carried state will be used to initialize the initial hidden state for the Hamiltonian dynamics branch and the direct vector field branch. A specific initialization method is to copy this carried state vector along the batch dimension to restore its shape, and then use it as the initial hidden state for the first time step of the next time window.

[0109] The neural network modeling method for non-adiabatic time-dependent density functional dynamics provided in this application proposes a time window-based carrying mechanism, which cleverly decouples information forward propagation and gradient backward propagation. While transmitting useful cross-window information, it ensures that the gradient only propagates within the window, thereby maintaining stable memory usage and improving training stability.

[0110] In some embodiments, this mechanism can be similarly applied to the memory exchange-related potential branch (MXC-Head), since it employs a standard recurrent neural network structure such as LSTM internally. Specifically, at the end of the current window, the final cell state of the LSTM is... and hidden state After averaging along the batch dimension, the initial state of the next window is saved, and the computational graph is also separated to form a slowly evolving cross-window memory without introducing long-range gradient paths, so as to balance non-adiabatic memory representation and numerical stability.

[0111] In some embodiments, the method further includes: Based on the loss of Hamiltonian dynamics branch, the loss of direct vector field branch, and the consistency constraint loss between Hamiltonian dynamics branch and direct vector field branch, the dynamics supervision loss is determined. The loss function of a three-head neural network is determined based on dynamic supervision loss and exchange-correlation potential supervision loss of memory exchange-correlation potential branch.

[0112] Specifically, the loss of the Hamiltonian dynamics branch ( This aims to supervise the Hamiltonian induced vector field generated by the Hamiltonian dynamics branch (HD-Head). Its calculation method involves taking the model output... Compare with a reference benchmark. The comparison metric can be the Mean Squared Error (MSE) loss, which is calculated... and The mean of the sum of squares of the differences between them. This loss term drives the Hamiltonian dynamics branch to learn a Hamiltonian that can generate the correct dynamical backbone.

[0113] Loss of the direct vector field branch ( This aims to supervise the direct vector field generated by the Direct Vector Field Branch (DVF-Head). Its calculation method is similar to that of the loss in the Hamiltonian dynamics branch, also involving the model output... The comparison is made with a reference benchmark. The metric function can also use mean squared error. This loss term drives the direct vector field branch to learn the correct dynamic evolution directly from the data.

[0114] Consistency constraint loss between Hamiltonian dynamics branch and direct vector field branch ( This approach aims to force the two dynamic prediction branches (HD-Head and DVF-Head) to work together and maintain consistency. It does not compare against an external reference, but rather directly compares the outputs of the two branches themselves. It is calculated by determining the mean square error between the Hamiltonian induced vector field and the direct vector field.

[0115] The consistency constraint loss plays a crucial regularization role. On one hand, when the Hamiltonian branch deviates from the true data due to its structural constraints, the consistency constraint loss "pulls" it towards the direct vector field branch, which is closer to the data. On the other hand, it also constrains the overly flexible direct vector field branch, preventing it from generating physically meaningless and drastic drifts in order to fit noise in the data, thus keeping it always near the physically meaningful Hamiltonian field. This "mutual attraction" mechanism enhances the physical interpretability of the learned energy and the overall robustness of the model.

[0116] Loss of memory exchange related potential branches ( This aims to supervise the exchange correlation potential predicted by the memory exchange correlation potential branch (MXC-Head). The calculation method is as follows: the model output... The potential is compared with the true exchange-correlation potential in the reference baseline. The metric function can also use mean squared error. This loss term drives the memory exchange-correlation potential branch to learn the correct, memory-effect-controlled nonadiabatic potential.

[0117] Finally, the four loss terms are weighted and summed to obtain the loss function of the three-head neural network. .

[0118] .

[0119] .

[0120] in, The weights used to calculate the consistency constraint loss; For dynamic monitoring loss; The weights for calculating the dynamic monitoring loss; The calculation weights for the supervisory loss of the exchange potential are used.

[0121] The neural network modeling method for non-adiabatic time-dependent density functional dynamics provided in this application provides a multi-objective, multi-task loss function design, which can ensure that the model can optimize the performance of each sub-task separately during the learning process, and promote the collaboration and alignment between different functional modules, so that the finally trained model achieves excellent comprehensive performance in multiple dimensions such as accuracy, stability, robustness and physical interpretability.

[0122] In some embodiments, after training is complete, given an initial phase space state sequence, the model outputs at each time step. and Output the zero-mean normalized value. .in Provides structurally consistent backbone dynamics. It provides data-driven correction; combined with the window carrying mechanism, it can obtain cross-window temporal context and improve the continuity of window boundaries without increasing the window length, thereby supporting stable rolling forecasts on longer time scales.

[0123] Figure 2 This is an architecture diagram of the three-head neural network provided in this application, such as... Figure 2 As shown, the three-head neural network provided in this application simultaneously learns time-dependent Kohn-Sham dynamics and non-adiabatic exchange-related potentials in a three-head collaborative manner, and unifies structure preservation, data correction, and time memory within the same framework. Compared with related technologies, this application has the following technical advantages in terms of accuracy, stability, interpretability, and engineering usability: (1) Balancing structural consistency and long-term propagation stability: The Hamiltonian dynamics head of this application outputs a scalar Hamiltonian and generates a symmetric vector field by fixing the symmetric matrix and automatically differentiating, so that the dynamics generation process naturally reflects the symmetric structural constraints, which is more conducive to suppressing error accumulation and drift in long-term propagation and is suitable for dynamics scenarios that require stable rolling prediction.

[0124] (2) Data-driven correction channel improves accuracy and robustness: This application sets a direct vector field head as a flexible reference channel and introduces a consistency term in the loss function to make the two ends mutually pull each other. When the Hamiltonian field deviates from the data, the consistency term will pull it back to the direct vector field that is closer to the data, while also avoiding unconstrained drift of the direct vector field, so that the learned energy has both physical interpretability and numerical accuracy. This design also allows the direct vector field to absorb non-Hamiltonian residual components, including non-ideal factors such as discrete errors or noise, improving robustness in non-adiabatic and noisy settings.

[0125] (3) Explicit memory potential prediction is more in line with non-adiabatic mechanism: This application adopts memory exchange-related potential modeling along the time axis, explicitly carries historical information through cyclic states, and applies zero-mean specification to the output to fix the specification degree of freedom of exchange-related potential. This specification process makes the learning objective unique at each time step, improves identifiability and stabilizes the optimization process, and avoids the network being interfered with by arbitrary bias.

[0126] (4) Two-way information exchange promotes branch coordination and alignment: This application introduces a hierarchical inference-based two-way information exchange between the Hamiltonian head and the direct vector field head, enabling the energy structure information of the higher level and the instantaneous dynamic information of the lower level to iteratively merge during the inference process, rather than simply outputting them in parallel. This mechanism helps to absorb local dynamic details while maintaining the main structure, thereby improving overall consistency and expressive power.

[0127] (5) Cross-window carrying mechanism balances long-range context and training efficiency: This application adopts windowed training for long sequences and introduces cross-window carrying of states. The carried states evolve slowly between windows to preserve long-range context, while the gradient is only backpropagated within the window and does not form a long-range gradient path. Thus, the non-adiabatic memory effect is captured while maintaining numerical stability and controllable resources, and it has good engineering feasibility.

[0128] The following description uses the application of the method of this application on a one-dimensional two-electron hydrogen scattering benchmark as an example. The experimental results are used to illustrate the effectiveness of the technical solution of this application on the benchmark task and do not constitute a limitation on the applicable scenarios.

[0129] Experimental results show that the method provided in this application achieves a lower and more stable error level in electron density reconstruction, with an average mean square error of approximately [missing value]. Compared to TDKSNN (a neural network that maintains Hamiltonian structure under the adiabatic assumption), the noise reduction is about an order of magnitude, and it outperforms TDKSNN variants with added memory modules and other comparative models, showing better tracking of sharp scattering features and less noise growth. The comparison results are shown in Table 1.

[0130] Table 1. Comparison of electron density fitting effects between the three-headed structure and other models.

[0131] In terms of reconstructing the exchange correlation potential, the method in this application can more completely capture the physically meaningful peaks and step structures in non-adiabatic scattering. The overall error is significantly lower than that of models such as HRM (hierarchical inference model) and DHN (denoised Hamiltonian neural network), and it maintains a lower error level and smaller variance over time. The comparison results are shown in Table 2.

[0132] Table 2. Comparison of the fitting cross-correlation potential effects of the three-headed structure with other models.

[0133] Furthermore, ablation experiments show that the three heads have complementary effects. Removing the Hamiltonian head causes the error to grow faster and fluctuate more strongly; removing the direct vector field head leads to high-frequency artifacts and decreased stability; and removing the memory exchange potential significantly amplifies the density error and causes it to grow rapidly over time, indirectly verifying the contribution of the structural design in this application to accuracy and long-term stability. The ablation experiment results of the related electron density fitting are shown in Table 3, corresponding to the complete three-head neural network, the ablation of the Hamiltonian dynamics branch, the ablation of the direct vector field branch, and the ablation of the memory exchange potential branch, respectively.

[0134] Table 3. Comparison of electron density fitting effects between the three-headed structure and the ablation model.

[0135] As can be seen from the above results, the technical solution of this application, while maintaining the consistency of the dynamic structure, introduces separable residual correction and explicit time memory, and is combined with bidirectional information exchange and cross-window carrying mechanism, so that it has better accuracy, stability and engineering deployability in non-adiabatic dynamic learning tasks.

[0136] The apparatus provided in the embodiments of this application is described below. The apparatus described below can be referred to in correspondence with the method described above.

[0137] Figure 3 This is a schematic diagram of the neural network modeling device for non-adiabatic time-dependent density functional dynamics provided in this application, as shown below. Figure 3 As shown, the device includes: The phase space representation and input embedding module 310 is used to construct a phase space state vector based on the real and imaginary parts of the occupied orbit coefficients, and obtain feature representations through the embedding layer; The Hamiltonian dynamics modeling module 320 is used to input the feature representation into the Hamiltonian dynamics branch of the three-head neural network to obtain the Hamiltonian induced vector field. The direct vector field modeling module 330 is used to input the feature representation into the direct vector field branch of the three-head neural network to obtain the direct vector field with representation data-driven correction. The memory exchange correlation potential modeling module 340 is used to input the feature representation into the memory exchange correlation potential branch of the three-head neural network, encode the historical information using the recurrent neural network to obtain the exchange correlation potential, and perform normalization processing on the exchange correlation potential. Among them, the Hamiltonian dynamics branch and the direct vector field branch are coupled through a two-way information interaction mechanism, and each branch maintains the continuity of long-term modeling through a cross-time window state transfer mechanism; the three-head neural network is jointly trained based on dynamic supervision loss and exchange correlation potential supervision loss.

[0138] The neural network modeling device for nonadiabatic time-dependent density functional dynamics provided in this application realizes a novel modeling paradigm for nonadiabatic quantum dynamics problems by constructing a three-headed neural network architecture including a Hamiltonian dynamics branch, a direct vector field branch, and a memory exchange-related potential branch. The memory exchange-related potential branch explicitly introduces a time memory effect using a recurrent neural network structure, solving the fundamental defects of the adiabatic approximation. The parallel setup of the Hamiltonian dynamics branch and the direct vector field branch, and the bidirectional information exchange mechanism between them, cleverly balance the relationship between the strict preservation of physical laws (structural consistency) and data-driven corrections for complex realities (accuracy and robustness). This integrated design enables the model to simultaneously model the structure, residuals, and memory within a unified framework, thereby achieving higher accuracy, better long-term stability, and stronger physical interpretability compared to existing technologies in simulating strongly nonequilibrium, long-term nonadiabatic dynamics.

[0139] In some embodiments, the device further includes: Loss construction module 350 is used to jointly optimize the above modules based on dynamic supervision loss and exchange correlation potential supervision loss.

[0140] Figure 4 This is a schematic diagram of the structure of the electronic device provided in this application, such as... Figure 4 As shown, the electronic device may include: a processor 410, a communications interface 420, a memory 430, and a communications bus 440, wherein the processor, communications interface, and memory communicate with each other via the communications bus. The processor can invoke logical commands stored in the memory to execute the methods described in the above embodiments, for example: The phase space state vector is constructed based on the real and imaginary parts of the orbital occupancy coefficients, and its feature representation is obtained through an embedding layer. The feature representation is input into the Hamiltonian dynamics branch of the tri-head neural network to obtain the Hamiltonian induced vector field. The feature representation is input into the direct vector field branch of the tri-head neural network to obtain the direct vector field representing the data-driven correction. The feature representation is input into the memory exchange correlation potential branch of the tri-head neural network, and historical information is encoded using a recurrent neural network to obtain the exchange correlation potential, which is then normalized. The Hamiltonian dynamics branch and the direct vector field branch are coupled through a bidirectional information exchange mechanism, and each branch maintains long-term modeling continuity through a cross-time window state transfer mechanism. The tri-head neural network is jointly trained based on dynamic supervision loss and exchange correlation potential supervision loss.

[0141] Furthermore, the logical commands in the aforementioned memory can be implemented as software functional units and sold or used as independent products, and can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several commands to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0142] The processor in the electronic device provided in this application embodiment can call logical instructions in the memory to implement the above method. Its specific implementation method is the same as the aforementioned method implementation method and can achieve the same beneficial effects, which will not be repeated here.

[0143] This application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is implemented to perform the methods provided in the above embodiments.

[0144] The specific implementation method is the same as the aforementioned method implementation method and can achieve the same beneficial effects, so it will not be repeated here.

[0145] This application provides a computer program product, including a computer program that, when executed by a processor, implements the method described above.

[0146] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0147] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0148] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A neural network modeling method for non-adiabatic time-dependent density functional dynamics, characterized in that, include: A phase space state vector is constructed based on the real and imaginary parts of the complex state coefficients of the occupied orbit, and a feature representation is obtained through an embedding layer. The feature representation is input into the Hamiltonian dynamics branch of the three-head neural network to obtain the Hamiltonian induced vector field. The feature representation is input into the direct vector field branch of the three-head neural network to obtain the direct vector field representing the data-driven correction. The feature representation is input into the memory exchange correlation potential branch of the three-head neural network, and the historical information is encoded using a recurrent neural network to obtain the exchange correlation potential. The exchange correlation potential is then normalized. The Hamiltonian dynamics branch and the direct vector field branch are coupled through a two-way information exchange mechanism, and each branch maintains long-term modeling continuity through a cross-time window state transfer mechanism; the three-head neural network is jointly trained based on dynamic supervision loss and exchange correlation potential supervision loss.

2. The neural network modeling method for non-adiabatic time-dependent density functional dynamics according to claim 1, characterized in that, The Hamiltonian dynamics branch and the direct vector field branch exchange information bidirectionally based on nested outer and inner loop iterations. In each outer loop iteration, an inner loop iteration is performed a preset number of times, where the preset number of times is at least once; In each inner loop iteration, the current hidden state of the Hamiltonian dynamics branch is combined with the feature representation to generate a guidance signal, and the hidden state of the direct vector field branch is updated based on the guidance signal. After completing the preset number of inner loop iterations, the hidden state of the Hamiltonian dynamics branch is updated based on the updated hidden state of the direct vector field branch.

3. The neural network modeling method for non-adiabatic time-dependent density functional dynamics according to claim 1, characterized in that, The step of inputting the feature representation into the Hamiltonian dynamics branch of a three-headed neural network to obtain the Hamiltonian induced vector field includes: The feature representation is input into the Hamiltonian dynamics branch, which then performs the following steps: The feature representation is processed based on a feedforward neural network to obtain a scalar Hamiltonian. The scalar Hamiltonian is differentiated, and the result of the differentiation is combined with the standard symplectic matrix to obtain the Hamiltonian induced vector field.

4. The neural network modeling method for non-adiabatic time-dependent density functional dynamics according to claim 1, characterized in that, The step of inputting the feature representation into the direct vector field branch of the three-head neural network to obtain a direct vector field representing the data-driven correction includes: The feature representation is input into the direct vector field branch, and the direct vector field branch performs the following steps: The hidden representation is obtained by mapping the feature representation based on the backbone network. The hidden representation is projected onto the first linear mapping layer to output a direct vector field representing the time derivative.

5. The neural network modeling method for non-adiabatic time-dependent density functional dynamics according to claim 1, characterized in that, The step of inputting the feature representation into the memory exchange-correlation potential branch of a three-headed neural network, encoding historical information using a recurrent neural network to obtain the exchange-correlation potential, and performing normalization processing on the exchange-correlation potential includes: The feature representation is input into the memory exchange correlation potential branch, and the memory exchange correlation potential branch performs the following steps: The feature representations are processed along the time axis using a recurrent neural network to obtain a sequence of hidden states; The hidden state sequence is mapped to a grid-resolved exchange correlation potential based on the second linear projection layer; The exchange correlation potential is normalized to zero mean.

6. The neural network modeling method for non-adiabatic time-dependent density functional dynamics according to any one of claims 1 to 5, characterized in that, The method further includes: The time series represented by the features is divided into multiple consecutive time windows along the time axis; After completing the processing of the current time window, the updated hidden states of the Hamiltonian dynamics branch and the direct vector field branch corresponding to the current time window are compressed along the batch processing dimension to obtain the carrying state of each branch. Perform a computation graph separation operation on the carried state to truncate the gradients backpropagating from subsequent time windows to the current time window; The carried state after separation by computational graph is used as the initial state of the next time window, and after being copied along the batch processing dimension, it is used to initialize the hidden state of the Hamiltonian dynamics branch and the direct vector field branch in the next time window.

7. The neural network modeling method for non-adiabatic time-dependent density functional dynamics according to any one of claims 1 to 5, characterized in that, The method further includes: Based on the loss of the Hamiltonian dynamics branch, the loss of the direct vector field branch, and the consistency constraint loss between the Hamiltonian dynamics branch and the direct vector field branch, the dynamics supervision loss is determined. The loss function of the three-head neural network is determined based on the dynamic supervision loss and the exchange correlation potential supervision loss of the memory exchange correlation potential branch.

8. A neural network modeling device for non-adiabatic time-dependent density functional dynamics, characterized in that, include: The phase space representation and input embedding module is used to construct a phase space state vector based on the real and imaginary parts of the complex state coefficients of the occupied orbit, and obtain feature representations through the embedding layer. The Hamiltonian dynamics modeling module is used to input the feature representation into the Hamiltonian dynamics branch of the three-head neural network to obtain the Hamiltonian induced vector field. The direct vector field modeling module is used to input the feature representation into the direct vector field branch of the three-head neural network to obtain a direct vector field representing the data-driven correction. The memory exchange correlation potential modeling module is used to input the feature representation into the memory exchange correlation potential branch of the three-head neural network, encode historical information using a recurrent neural network to obtain the exchange correlation potential, and perform normalization processing on the exchange correlation potential. The Hamiltonian dynamics branch and the direct vector field branch are coupled through a two-way information exchange mechanism, and each branch maintains long-term modeling continuity through a cross-time window state transfer mechanism; the three-head neural network is jointly trained based on dynamic supervision loss and exchange correlation potential supervision loss.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the neural network modeling method for non-adiabatic time-dependent density functional dynamics as described in any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the neural network modeling method for non-adiabatic time-dependent density functional dynamics as described in any one of claims 1 to 7.

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