Multiscale modelling of ferroelectrics using a physics-informed neural network driven by molecular dynamics data: parameter identification and field reconstruction
A physics-informed neural network (PINN) framework is developed, in which the loss function consists of MD-data penalty and partial difference equation (PDE) constraints, which provides an effective methodology for multiscale bridging between atomistic and continuum descriptions for perovskite ferroelectric materials.
Abstract
In multiscale modeling of ferroelectric materials, a fundamental challenge is to transfer discrete atomistic information into a continuum phase-field model (PFM) while retaining an accurate description of mesoscale behavior. In this paper, a physics-informed neural network (PINN) framework is developed, in which the loss function consists of MD-data penalty and partial difference equation (PDE) constraints. By minimizing the loss function, the model not only reconstructs the polarization field along with the full coupled electromechanical response, including strain, stress, electric field, and energy landscape at the continuum scale, but also identifies critical parameters required for the PFM, including the characteristic energy density, characteristic length factor, anisotropy factor, and Landau polynomial coefficients. By using the PINN-predicted parameters to solve the corresponding PDEs within a finite element framework, we perform a cross-verification showing that the two numerical implementations yield consistent results. In addition, the transferability of the learned parameters is further evaluated through extended three-dimensional PF simulations under external tensile and bending loading, in which the domain expansion, shrinkage, annihilation, and fragmentation are in agreement with the corresponding experimental observations. This framework provides an effective methodology for multiscale bridging between atomistic and continuum descriptions for perovskite ferroelectric materials.
To address the complexities associated with highly nonlinear phase transitions in subbase materials subjected to unidirectional freezing—where direct observation of internal states is challenging—and the limitations of conventional numerical methods in concurrently reconstructing multiphysical fields from sparse experimental data, this study investigates saturated subbase materials from the Dashixia Project. Laboratory freezing experiments were performed, and a two-dimensional axisymmetric physics-informed neural network (PINN) model integrating thermomechanical behavior, phase transition, and deformation was developed. The model incorporated the heat conduction equation (accounting for latent heat), the freezing fraction relaxation equation, and the effective deformation equation into the loss function, employing a continuous freezing fraction to represent phase-change phenomena. Additionally, constraints on the average displacement of the top surface, enhanced sampling near the freezing front, and a dynamic weighting strategy were introduced to improve model performance. This approach enabled the simultaneous prediction of temperature, freezing fraction, and displacement fields. The model achieved a temperature prediction root mean square error (RMSE) of 4.112 °C with an R2 of 0.600, and a top-surface displacement prediction RMSE of 0.0051 with an R2 of 0.993. Observations indicated that the freezing front predominantly progressed from the top downward, while the displacement field exhibited a partitioned pattern characterized by negative displacement in the lower region and positive displacement in the upper region. The proposed methodology offers a novel framework for multi-field reconstruction and frost heave prediction in subgrade materials under conditions of limited observational data.
Anshuang Su, Heng Zhou, Mingwei Hai et al.· Applied Sciences· 0 citations
We present a high-dimensional neural network potential (HDNNP) for the martensitic phase of the NiTi shape-memory alloy trained to density functional theory (DFT) data. A central aspect of this work is the systematic validation of the potential with respect to the underlying DFT reference method for key properties governing structural evolution, including equilibrium crystal structures, elastic constants, generalized-stacking fault energies, and vibrational spectra. The HDNNP accurately describes the relative stability of the B19$^\prime$ and B33 phases, including subtle energy differences on the order of meV/atom. The predicted stacking-fault energy landscape is strongly anisotropic and reveals a preferential shear pathway, providing atomistic insight into deformation and twinning mechanisms. Finite-temperature molecular dynamics simulations further enable the investigation of unconstrained structural evolution as a function of temperature. Overall, the developed HDNNP provides a robust basis for atomistic simulations of the complex structural and functional behavior of martensitic NiTi systems containing hundreds of thousands of atoms on nanosecond time scales.
P. Jaroš, Petr Sedlák, Petr Šesták et al.· 0 citations
Predicting how passive oxide films grow and break down is central to corrosion science and the long-term integrity of structural alloys, and the point defect model (PDM) is the standard kinetic description: a stiff, coupled system of Nernst–Planck, Poisson, and Butler–Volmer equations on a moving boundary; solving it conventionally requires specialized finite-element (FEM) solvers and identifying its kinetic parameters requires costly experimental campaigns. Physics-informed neural networks (PINNs) are compelling here because they natively assimilate data and invert for unknown parameters, so one measurement can replace an FEM solution and yield what kinetics FEM cannot. We show that PINNs solve the PDM and recover its parameters from sparse data. The problem is difficult for reasons common to stiff multiphysics systems: widely separated scales, stiff boundary conditions, and convergence to non-physical solution branches. We address these with physics-based non-dimensionalization, which extends stable simulation from about 1 to 250 h; NTK adaptive weighting, which compresses a four-to-six-order loss imbalance to roughly one; and a single validated anchor that selects the physical branch and brings film-thickness error to below 2.2% at all five potentials. Stiff boundary-condition enforcement remains an open problem. Robustness comes from resampling the anchor each step; accuracy saturates beyond ten anchors; and the physics loss tolerates 5% measurement noise. Crucially, recoverability tracks stiffness: a boundary-stiff kinetic constant is identifiable from film-thickness data while a weakly coupled interior coefficient is not. By turning sparse measurements into full fields and inferred kinetics, this approach reduces the experimental and computational burden of characterizing passive-film growth.
We propose an unsupervised learning framework for calibrating a physics-augmented neural network (PANN) for small-strain viscoelasticity via full-field data. It only requires quantities that are directly accessible in real experiments for training, namely global reaction forces and surface displacements. The underlying PANN is embedded in the generalized standard materials theory, in which two scalar-valued potentials render the constitutive model thermodynamically consistent by construction, while invariant-based representations of the free energy and the dual dissipation potential additionally ensure material symmetry. Considering a thin specimen under the plane stress assumption, we formulate a constrained optimization problem based on the equilibrium gap method in combination with quasi-Newton optimizers and automatic differentiation. Thereby, the unknown out-of-plane strain follows from the plane stress condition and the evolution of the internal variables is captured by an implicit time integration scheme. The resulting system of nonlinear equations is solved via a local Newton iteration at quadrature point and time step. To drastically reduce the computational cost of training, the backward adjoint method is employed to compute the gradient of the target loss, instead of backpropagating through all Newton iteration steps. The proposed framework is demonstrated for synthetic data, including noisy displacements and forces, showing excellent agreement across a wide range of deformation rates and load paths.
Brain M. Riemer, Markus Kästner, Karl A. Kalina· 0 citations
In this study, a Physics-Informed Neural Network (PINN) is proposed for solving the one-dimensional diffusion equation under the oscillatory sine boundary condition. The PINN method differs from other numerical techniques that consume substantial computational power and require mesh construction since the physical equations and boundary conditions are integrated directly into the network architecture. This is accomplished through constructing a neural network via TensorFlow and employing a loss function that encompasses the physics equations and boundary conditions. The output of the PINN is then compared with the exact solution, showing remarkable consistency and numerical precision. The model has a consistent error of less than 0.02 and an RMSE of approximately 0.01, with absolute errors ranging from 10−3. Not only does the model demonstrate numerical superiority, but it can also accurately identify the phase and amplitude properties of the oscillatory solutions. In addition, it successfully transitions between areas of steep gradients at boundaries and regions of oscillatory damping to a steady state while maintaining temporal stability during training. Further, validation via topographic comparison of the three-dimensional model shows that the proposed numerical model retains the structure and physics of the analytical solution. In general, the results demonstrate the success of PINNs in providing an efficient and robust numerical approach for solving partial differential equations compared to classical and analytical approaches.
Venkata Koushal Challapalli, P. Puvaneswari· 2026 4th International Confe...· 0 citations
The results demonstrate that the mPINN architecture functions as a reliable, physics-constrained ML framework capable of delivering high-fidelity trajectory predictions for complex multi-body molecular systems.
T. Muther, Vuong Van Pham, A. K. Dahaghi· Machine Learning: Science an...· 0 citations
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