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Parameterized Physics-informed Neural Networks for Parameterized PDEs

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arxiv 2408.09446 v1 pith:XTYN6B6S submitted 2024-08-18 cs.LG cs.NAmath.NAphysics.comp-ph

classification cs.LGcs.NAmath.NAphysics.comp-ph
keywords parameterizedpdesinnsnetworksneuralphysics-informedneedparameter
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

Complex physical systems are often described by partial differential equations (PDEs) that depend on parameters such as the Reynolds number in fluid mechanics. In applications such as design optimization or uncertainty quantification, solutions of those PDEs need to be evaluated at numerous points in the parameter space. While physics-informed neural networks (PINNs) have emerged as a new strong competitor as a surrogate, their usage in this scenario remains underexplored due to the inherent need for repetitive and time-consuming training. In this paper, we address this problem by proposing a novel extension, parameterized physics-informed neural networks (P$^2$INNs). P$^2$INNs enable modeling the solutions of parameterized PDEs via explicitly encoding a latent representation of PDE parameters. With the extensive empirical evaluation, we demonstrate that P$^2$INNs outperform the baselines both in accuracy and parameter efficiency on benchmark 1D and 2D parameterized PDEs and are also effective in overcoming the known "failure modes".

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Cited by 6 Pith papers

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

  1. Material-agnostic temperature field prediction for metal additive manufacturing via a parametric PINN framework

    cs.LG 2026-04 unverdicted novelty 6.0 of 10

    One physics-informed network trained on the heat equation, not labeled data, predicts laser-scan temperature fields for unseen alloys including copper with ~1% relative error.

  2. Disentangled Latent Dynamics Manifold Fusion for Solving Parameterized PDEs

    cs.LG 2026-03 unverdicted novelty 6.0 of 10

    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.

  3. Governing Equation Discovery from Data Based on Differential Invariants

    cs.LG 2025-05 conditional novelty 6.0 of 10

    PDE discovery guided by symmetry can be done by building the SINDy library from the differential invariants of the PDE's symmetry group, which shrinks the search space and improves success rates.

  4. IP-Basis PINNs: Efficient Multi-Query Inverse Parameter Estimation

    cs.LG 2025-09 conditional novelty 5.0 of 10

    A pre-trained basis network enables fast multi-query inverse parameter estimation by fitting only a linear readout online, demonstrated on harmonic oscillators, Lotka-Volterra, and quantum harmonic oscillator.

  5. Physics-informed machine learning surrogate for scalable simulation of thermal histories during wire-arc directed energy deposition

    cs.CE 2025-07 conditional novelty 5.0 of 10

    A data-free physics-informed neural network matches finite-element thermal histories of wire-arc directed energy deposition to about 7% relative L2 error, reporting up to 98.6% compute-time reduction versus a fine-mes...

  6. Performance of Krotov, PRONTO and PINN for optimal control of quantum gates

    quant-ph 2026-07 conditional novelty 4.0 of 10

    An enhanced PINN with Fourier features, per-epoch normalization, and pretraining designs high-fidelity quantum gates comparable to Krotov and PRONTO, but more slowly and with overclaimed headline results.

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