PIANO: Physics Informed Autoregressive Network

• URL: http://arxiv.org/abs/2508.16235v1
• Date: Fri, 22 Aug 2025 09:12:47 GMT
• Title: PIANO: Physics Informed Autoregressive Network
• Authors: Mayank Nagda, Jephte Abijuru, Phil Ostheimer, Marius Kloft, Sophie Fellenz,
• Abstract summary: We introduce Physics-Informed Autoregressive Networks (PIANO) -- a framework that redesigns PINNs to model dynamical systems.<n>We show PIANO achieves state-of-the-art performance, significantly improving accuracy and stability over existing methods.
• Score: 23.37066841328924
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Solving time-dependent partial differential equations (PDEs) is fundamental to modeling critical phenomena across science and engineering. Physics-Informed Neural Networks (PINNs) solve PDEs using deep learning. However, PINNs perform pointwise predictions that neglect the autoregressive property of dynamical systems, leading to instabilities and inaccurate predictions. We introduce Physics-Informed Autoregressive Networks (PIANO) -- a framework that redesigns PINNs to model dynamical systems. PIANO operates autoregressively, explicitly conditioning future predictions on the past. It is trained through a self-supervised rollout mechanism while enforcing physical constraints. We present a rigorous theoretical analysis demonstrating that PINNs suffer from temporal instability, while PIANO achieves stability through autoregressive modeling. Extensive experiments on challenging time-dependent PDEs demonstrate that PIANO achieves state-of-the-art performance, significantly improving accuracy and stability over existing methods. We further show that PIANO outperforms existing methods in weather forecasting.

Related papers

• Physics-Informed Neural Operators for Cardiac Electrophysiology [2.789396703574285]
  We propose a Physics-Informed Neural Operator (PINO) approach to solve PDE problems in cardiac electrophysiology.<n>Our results show that PINO models can accurately reproduce cardiac EP dynamics over extended time horizons and across multiple propagation scenarios.<n>These advantages come with a significant reduction in simulation time compared to numerical PDE solvers.
  arXiv  Detail & Related papers  (2025-11-11T16:28:56Z)
• Physics-informed Temporal Alignment for Auto-regressive PDE Foundation Models [2.57401182252473]
  We propose physics-informed temporal alignment (PITA), a self-supervised learning framework inspired by inverse problem solving.<n>PITA aligns the physical dynamics discovered at different time steps on each given PDE trajectory by integrating physics-informed constraints into the self-supervision signal.<n>Experiments show that PITA significantly enhances the accuracy and robustness of existing foundation models on diverse time-dependent PDE data.
  arXiv  Detail & Related papers  (2025-05-16T07:08:47Z)
• Physics-Informed Latent Neural Operator for Real-time Predictions of time-dependent parametric PDEs [0.0]
  Deep operator network (DeepONet) has shown promise as surrogate models for systems governed by partial differential equations (PDEs)<n>In this work, we propose PI-Latent-NO, a physics-informed latent neural operator framework that integrates governing physics directly into the learning process.
  arXiv  Detail & Related papers  (2025-01-14T20:38:30Z)
• Advancing Generalization in PINNs through Latent-Space Representations [71.86401914779019]
  Physics-informed neural networks (PINNs) have made significant strides in modeling dynamical systems governed by partial differential equations (PDEs)<n>We propose PIDO, a novel physics-informed neural PDE solver designed to generalize effectively across diverse PDE configurations.<n>We validate PIDO on a range of benchmarks, including 1D combined equations and 2D Navier-Stokes equations.
  arXiv  Detail & Related papers  (2024-11-28T13:16:20Z)
• PhyMPGN: Physics-encoded Message Passing Graph Network for spatiotemporal PDE systems [31.006807854698376]
  We propose a new graph learning approach, namely, Physics-encoded Message Passing Graph Network (PhyMPGN)<n>We incorporate a GNN into a numerical integrator to approximate the temporal marching of partialtemporal dynamics for a given PDE system.<n>PhyMPGN is capable of accurately predicting various types of operatortemporal dynamics on coarse unstructured meshes.
  arXiv  Detail & Related papers  (2024-10-02T08:54:18Z)
• Physics-guided Active Sample Reweighting for Urban Flow Prediction [75.24539704456791]
  Urban flow prediction is a nuanced-temporal modeling that estimates the throughput of transportation services like buses, taxis and ride-driven models. Some recent prediction solutions bring remedies with the notion of physics-guided machine learning (PGML) We develop a atized physics-guided network (PN), and propose a data-aware framework Physics-guided Active Sample Reweighting (P-GASR)
  arXiv  Detail & Related papers  (2024-07-18T15:44:23Z)
• SEGNO: Generalizing Equivariant Graph Neural Networks with Physical Inductive Biases [66.61789780666727]
  We show how the second-order continuity can be incorporated into GNNs while maintaining the equivariant property. We also offer theoretical insights into SEGNO, highlighting that it can learn a unique trajectory between adjacent states. Our model yields a significant improvement over the state-of-the-art baselines.
  arXiv  Detail & Related papers  (2023-08-25T07:15:58Z)
• Learning Neural Constitutive Laws From Motion Observations for Generalizable PDE Dynamics [97.38308257547186]
  Many NN approaches learn an end-to-end model that implicitly models both the governing PDE and material models. We argue that the governing PDEs are often well-known and should be explicitly enforced rather than learned. We introduce a new framework termed "Neural Constitutive Laws" (NCLaw) which utilizes a network architecture that strictly guarantees standard priors.
  arXiv  Detail & Related papers  (2023-04-27T17:42:24Z)
• Physics Informed Neural Network for Dynamic Stress Prediction [10.588266927411434]
  A Physics Informed Neural Network (PINN) model is proposed to predict the entire sequence of stress distribution based on Finite Element simulations. Using automatic differentiation, we embed a PDE into a deep neural network's loss function to incorporate information from measurements and PDEs. The PINN-Stress model can predict the sequence of stress distribution in almost real-time and can generalize better than the model without PINN.
  arXiv  Detail & Related papers  (2022-11-28T16:03:21Z)
• Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamics [11.981731023317945]
  Physics-informed deep learning (PiDL) addresses these challenges by incorporating physical principles into the model. We propose to leverage physics prior knowledge by baking'' the discretized governing equations into the neural network architecture. This method, embedding discretized PDEs through convolutional residual networks in a multi-resolution setting, largely improves the generalizability and long-term prediction.
  arXiv  Detail & Related papers  (2022-05-09T01:27:58Z)
• Neural Operator with Regularity Structure for Modeling Dynamics Driven by SPDEs [70.51212431290611]
  Partial differential equations (SPDEs) are significant tools for modeling dynamics in many areas including atmospheric sciences and physics. We propose the Neural Operator with Regularity Structure (NORS) which incorporates the feature vectors for modeling dynamics driven by SPDEs. We conduct experiments on various of SPDEs including the dynamic Phi41 model and the 2d Navier-Stokes equation.
  arXiv  Detail & Related papers  (2022-04-13T08:53:41Z)
• Characterizing possible failure modes in physics-informed neural networks [55.83255669840384]
  Recent work in scientific machine learning has developed so-called physics-informed neural network (PINN) models. We demonstrate that, while existing PINN methodologies can learn good models for relatively trivial problems, they can easily fail to learn relevant physical phenomena even for simple PDEs. We show that these possible failure modes are not due to the lack of expressivity in the NN architecture, but that the PINN's setup makes the loss landscape very hard to optimize.
  arXiv  Detail & Related papers  (2021-09-02T16:06:45Z)
• Stochastically forced ensemble dynamic mode decomposition for forecasting and analysis of near-periodic systems [65.44033635330604]
  We introduce a novel load forecasting method in which observed dynamics are modeled as a forced linear system. We show that its use of intrinsic linear dynamics offers a number of desirable properties in terms of interpretability and parsimony. Results are presented for a test case using load data from an electrical grid.
  arXiv  Detail & Related papers  (2020-10-08T20:25:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.