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Respecting causality is all you need for training physics-informed neural networks

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arxiv 2203.07404 v1 pith:NKDWF7DI submitted 2022-03-14 cs.LG cs.NAmath.NAnlin.CDphysics.flu-dynstat.ML

Sifan Wang , Shyam Sankaran , Paris Perdikaris This is my paper
classification cs.LGcs.NAmath.NAnlin.CDphysics.flu-dynstat.ML
keywords pinnschaoticsystemsbeencausalityexistingformulationsmodel
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While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this date PINNs have not been successful in simulating dynamical systems whose solution exhibits multi-scale, chaotic or turbulent behavior. In this work we attribute this shortcoming to the inability of existing PINNs formulations to respect the spatio-temporal causal structure that is inherent to the evolution of physical systems. We argue that this is a fundamental limitation and a key source of error that can ultimately steer PINN models to converge towards erroneous solutions. We address this pathology by proposing a simple re-formulation of PINNs loss functions that can explicitly account for physical causality during model training. We demonstrate that this simple modification alone is enough to introduce significant accuracy improvements, as well as a practical quantitative mechanism for assessing the convergence of a PINNs model. We provide state-of-the-art numerical results across a series of benchmarks for which existing PINNs formulations fail, including the chaotic Lorenz system, the Kuramoto-Sivashinsky equation in the chaotic regime, and the Navier-Stokes equations in the turbulent regime. To the best of our knowledge, this is the first time that PINNs have been successful in simulating such systems, introducing new opportunities for their applicability to problems of industrial complexity.

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Cited by 10 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 18 citations worldwide. Full citation record

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  2. Disentangled Latent Dynamics Manifold Fusion for Solving Parameterized PDEs

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    DLDMF maps PDE parameters to latent embeddings that drive a Neural ODE and a shared decoder, improving parameter generalization and long-horizon temporal extrapolation over prior neural surrogates.

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  4. Transformed Diffusion-Wave fPINNs: Enhancing Computing Efficiency for PINNs Solving Time-Fractional Diffusion-Wave Equations

    math.NA 2025-06 conditional novelty 6.0 of 10

    A new representation of the Caputo derivative for order 1<α<2 avoids shifted first-derivative evaluations in PINNs, giving computational savings with comparable accuracy in the tested smooth cases.

  5. Variational Boosting for Physics-Informed Neural Networks

    cs.LG 2026-07 conditional novelty 5.0 of 10

    A staged boosting method for PINNs, using small correction networks and per-stage Newton/CG optimization, converges on several stiff ODE/PDE benchmarks where monolithic PINNs do not, while being slower on easy problems.

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    Energy Manifold Natural Gradient Descent (EMNGD) defines the energy natural gradient on a Riemannian parameter manifold and proves it equals the energy-metric projection of the function-space Newton step.

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    Meta-learning on easy PDE tasks plus a layer-wise gating schedule reduces extrapolation error by about 91% relative to six PINN baselines on hard convection, Helmholtz, and Navier-Stokes benchmarks.

  8. Neural Multiscale Decomposition for Solving The Nonlinear Klein-Gordon Equation with Time Oscillation

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  9. Low-rank adaptive physics-informed HyperDeepONets for solving differential equations

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    A review proposing a liver radioembolization digital twin that combines CFD with physics-informed neural networks to plan microsphere delivery.

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