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Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next

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arxiv 2201.05624 v4 pith:DMGCD6MO submitted 2022-01-14 cs.LG cs.AIcs.NAmath.NAphysics.data-an

classification cs.LGcs.AIcs.NAmath.NAphysics.data-an
keywords neuralnetworksequationspinnpinnslearninglikenetwork
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Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself. PINNs are nowadays used to solve PDEs, fractional equations, integral-differential equations, and stochastic PDEs. This novel methodology has arisen as a multi-task learning framework in which a NN must fit observed data while reducing a PDE residual. This article provides a comprehensive review of the literature on PINNs: while the primary goal of the study was to characterize these networks and their related advantages and disadvantages. The review also attempts to incorporate publications on a broader range of collocation-based physics informed neural networks, which stars form the vanilla PINN, as well as many other variants, such as physics-constrained neural networks (PCNN), variational hp-VPINN, and conservative PINN (CPINN). The study indicates that most research has focused on customizing the PINN through different activation functions, gradient optimization techniques, neural network structures, and loss function structures. Despite the wide range of applications for which PINNs have been used, by demonstrating their ability to be more feasible in some contexts than classical numerical techniques like Finite Element Method (FEM), advancements are still possible, most notably theoretical issues that remain unresolved.

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Cited by 8 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 83 citations worldwide. Full citation record

  1. Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics

    cs.LG 2026-07 conditional novelty 6.5 of 10

    LLPNNs recover latent Lie–Poisson momentum dynamics from observable configuration and velocity data by exploiting conserved spatial momentum and coadjoint reconstruction.

  2. Unbiased Data-Driven Determination of the Nuclear Dipole Amplitude in the Color Glass Condensate

    hep-ph 2026-07 conditional novelty 6.0 of 10

    The 208Pb dipole amplitude is learned from R_pPb and coherent J/ψ photoproduction data with the BK equation embedded in training, giving Q²_s0(Pb)/Q²_s0(p) = 3.17 and an MV-type initial condition.

  3. LithoFormer: A Robust Framework for Stratigraphic Inference via Transformers

    cs.LG 2026-07 conditional novelty 6.0 of 10

    A whole-log transformer with a geology-aware loss predicts stratigraphic zones and marker depths, beating sliding-window baselines on three well-log datasets.

  4. Physics-Informed Global Extraction of the Universal Small-$x$ Dipole Amplitude

    hep-ph 2026-03 conditional novelty 6.0 of 10

    A nonparametric PINN-constrained dipole amplitude simultaneously describes HERA total/charm DIS and J/psi photoproduction while maintaining Fourier positivity, unlike analytic MV-type fits.

  5. LIGO-PINN: Learned Initialization via Gated Optimization to Alleviate Convergence Failures in Physics Informed Neural Networks

    cs.LG 2026-07 conditional novelty 5.0 of 10

    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.

  6. Physics-Informed Residual Deep Learning for Constitutive Modeling of Hot Deformation and Dynamic Recrystallization in a Mo-Rich $\alpha+\beta$ Titanium Alloy

    cond-mat.mtrl-sci 2026-07 conditional novelty 5.0 of 10

    A DRX-aware physics-constrained neural network reproduces hot-compression flow stress of Ti–6Al–4Mo–1V–0.1Si with R²≈0.985, but its recrystallization fraction is a soft-prior artifact rather than an independently vali...

  7. Evaluation of Neural Surrogates for Physical Modelling Synthesis of Nonlinear Elastic Plates

    cs.SD 2025-07 conditional novelty 4.0 of 10

    On a Berger plate benchmark, state-of-the-art neural surrogates fail in long autoregressive rollouts, and time-domain error metrics miss the resulting spectral errors.

  8. Applications and Manipulations of Physics-Informed Neural Networks in Solving Differential Equations

    cs.LG 2025-07 reject novelty 2.0 of 10

    The paper demonstrates standard PINN fitting for polynomial and heat-equation problems and claims PINNs are less sensitive than finite-difference methods to the CFL stability condition.

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