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Physics-Informed Neural Networks and Extensions

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arxiv 2408.16806 v1 pith:UVVLQQN5 submitted 2024-08-29 cs.LG cs.AI

Maziar Raissi , Paris Perdikaris , Nazanin Ahmadi , George Em Karniadakis This is my paper · ORCID
classification cs.LGcs.AI
keywords extensionsnetworksneuralphysics-informedbecomedata-drivendifferentialdiscovery
verification ladder T0 review T1 audit T2 compute T3 formal
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In this paper, we review the new method Physics-Informed Neural Networks (PINNs) that has become the main pillar in scientific machine learning, we present recent practical extensions, and provide a specific example in data-driven discovery of governing differential equations.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Ramanujan Challenge For AI

    math.HO 2026-06 accept novelty 6.5 of 10

    A benchmark of new continued fractions, recurrences, series and integrals for classical constants, split into encrypted-proof problems and open conjectures for testing AI mathematical reasoning.

  2. Can AI Follow In Einstein's Footsteps?

    physics.hist-ph 2026-07 conditional novelty 6.0 of 10

    AI for physics has moved from explicit equation discovery to black-box prediction, a trajectory the authors argue reverses the historical progression of human physics, leaving the invention of new mathematical framewo...

  3. Physics-Informed Neural Networks for Modeling the Martian Induced Magnetosphere

    astro-ph.EP 2025-12 conditional novelty 6.0 of 10

    A physics-informed neural network conditioned on solar wind parameters reconstructs the 3D magnetic field of Mars's induced magnetosphere.

  4. DEF: Diffusion-augmented Ensemble Forecasting

    cs.LG 2025-06 conditional novelty 6.0 of 10

    A conditional diffusion model that generates perturbed initial states can turn any deterministic neural weather forecast model into an ensemble, with measured error reduction on a single ERA5 case study.

  5. A Unified Framework for Simultaneous Parameter and Function Discovery in Differential Equations

    cs.LG 2025-05 reject novelty 4.0 of 10

    The paper proves identifiability conditions for ODE inverse problems with one unknown constant and one unknown function, and adds approximate error bounds when data points are close but not identical.

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