mlsanityData to 7 Oct 2026

DPM: A Novel Training Method for Physics-Informed Neural Networks in Extrapolation

arXiv 2012.02681 ↗First posted 4 Dec 2020cs.LG cs.AIcited by 45

Not on the map. Why?

Abstract (arXiv)

We present a method for learning dynamics of complex physical processes described by time-dependent nonlinear partial differential equations (PDEs). Our particular interest lies in extrapolating solutions in time beyond the range of temporal domain used in training. Our choice for a baseline method is physics-informed neural network (PINN) [Raissi et al., J. Comput. Phys., 378:686--707, 2019] because the method parameterizes not only the solutions but also the equations that describe the dynamics of physical processes. We demonstrate that PINN performs poorly on extrapolation tasks in many benchmark problems. To address this, we propose a novel method for better training PINN and demonstrate that our newly enhanced PINNs can accurately extrapolate solutions in time. Our method shows up to 72% smaller errors than existing methods in terms of the standard L2-norm metric.

Key facts. Cited by 45 papers in the map (data through 7 Oct 2026). First posted on arXiv 4 Dec 2020.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 10; 2023: 9; 2024: 6; 2025: 11; 2026: 8.

45 papers.

Sort:

By area:

  1. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 603
  2. 2022When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learningcited by 64
  3. 2023Hypernetwork-based Meta-Learning for Low-Rank Physics-Informed Neural Networkscited by 42
  4. 2022Enhanced Physics-Informed Neural Networks with Augmented Lagrangian Relaxation Method (AL-PINNs)cited by 35
  5. 2022Implicit Neural Spatial Representations for Time-dependent PDEscited by 35
  6. 2024Parameterized Physics-informed Neural Networks for Parameterized PDEscited by 35
  7. 2024Dual Cone Gradient Descent for Training Physics-Informed Neural Networkscited by 21
  8. 2025Recurrent Neural Operators: Stable Long-Term PDE Predictioncited by 15
  9. 2021SPATE-GAN: Improved Generative Modeling of Dynamic Spatio-Temporal Patterns with an Autoregressive Embedding Losscited by 13
  10. 2022A Unified Hard-Constraint Framework for Solving Geometrically Complex PDEscited by 11
  11. 2023Efficient Error Certification for Physics-Informed Neural Networkscited by 10
  12. 2022Physical Activation Functions (PAFs): An Approach for More Efficient Induction of Physics into Physics-Informed Neural Networks (PINNs)cited by 9
33 more
  1. 2023Neural oscillators for generalization of physics-informed machine learningcited by 9
  2. 2023Understanding and Mitigating Extrapolation Failures in Physics-Informed Neural Networkscited by 8
  3. 2023Transfer learning for improved generalizability in causal physics-informed neural networks for beam simulationscited by 8
  4. 2022TimeKit: A Time-series Forecasting-based Upgrade Kit for Collaborative Filteringcited by 7
  5. 2023Personalized Predictions of Glioblastoma Infiltration: Mathematical Models, Physics-Informed Neural Networks and Multimodal Scanscited by 7
  6. 2025ATHENA: Agentic Team for Hierarchical Evolutionary Numerical Algorithmscited by 7
  7. 2022Deep Random Vortex Method for Simulation and Inference of Navier-Stokes Equationscited by 5
  8. 2024Frequency-adaptive Multi-scale Deep Neural Networkscited by 5
  9. 2025Dual-Balancing for Physics-Informed Neural Networkscited by 5
  10. 2025Network-wide Freeway Traffic Estimation Using Sparse Sensor Data: A Dirichlet Graph Auto-Encoder Approachcited by 4
  11. 2025On the under-reaching phenomenon in message-passing neural PDE solvers: revisiting the CFL conditioncited by 4
  12. 2023GRINN: A Physics-Informed Neural Network for solving hydrodynamic systems in the presence of self-gravitycited by 3
  13. 2024Collocation-based Robust Variational Physics-Informed Neural Networks (CRVPINN)cited by 3
  14. 2025Neuro-Spectral Architectures for Causal Physics-Informed Networkscited by 3
  15. 2022Physics-Informed Graph Learningcited by 2
  16. 2022Modelling of physical systems with a Hopf bifurcation using mechanistic models and machine learningcited by 2
  17. 2025MoGERNN: An Inductive Traffic Predictor for Unobserved Locationscited by 2
  18. 2025A Generalizable Physics-Enhanced State Space Model for Long-Term Dynamics Forecasting in Complex Environmentscited by 2
  19. 2023Enabling Hard Constraints in Differentiable Neural Network and Accelerator Co-Explorationcited by 0
  20. 2023Bayesian Reasoning for Physics Informed Neural Networkscited by 0
  21. 2024Neural Networks-based Random Vortex Methods for Modelling Incompressible Flowscited by 0
  22. 2024Invariant deep neural networks under the finite group for solving partial differential equationscited by 0
  23. 2025Improving physics-informed neural network extrapolation via transfer learning and adaptive activation functionscited by 0
  24. 2025Blending data and physics for reduced-order modeling of systems with spatiotemporal chaotic dynamicscited by 0
  25. 2025Limitations of Physics-Informed Neural Networks: a Study on Smart Grid Surrogationcited by 0
  26. 2026BEACONS: Bounded-Error, Algebraically-Composable Neural Solvers for Partial Differential Equationscited by 0
  27. 2026Python library supporting Discrete Variational Formulations and training solutions with Collocation-based Robust Variational Physics Informed Neural Networks (DVF-CRVPINN)cited by 0
  28. 2026Transferable Physics-Informed Representations via Closed-Form Head Adaptationcited by 0
  29. 2026Metropolis-Scale Resilient and Trustworthy Traffic Flow Inference Using Multi-Source Datacited by 0
  30. 2026LIGO-PINN: Learned Initialization via Gated Optimization to Alleviate Convergence Failures in Physics Informed Neural Networkscited by 0
  31. 2026Perturbative-NeuSA: A Structured Spectral Framework for Time-Dependent PDEscited by 0
  32. 2026Physics-Informed Foresight Pruning for Sparse PINN Solvers of Nonlinear PDEscited by 0
  33. 2026Development and Validation of a Physics-Guided Machine Learning Extrapolation Framework Using a Classical Transient Diffusion Benchmarkcited by 0