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This paper proposes a Physics-Informed Error Field Learning (PIEFL) framework for Physics-Informed Neural Networks, introducing an auxiliary error network to improve solution accuracy in solving partial differential equations under computational constraints.
The paper introduces a 'wrong-physics backdoor' poisoning attack on neural PDE operators, where triggered inputs cause models to output valid solutions for alternate physical parameters, highlighting a critical security vulnerability in reusable solver archives.
The paper presents STCO, a conditional neural operator for prescribed-condition operator learning in time-dependent PDEs, which improves prediction accuracy by incorporating various condition fields and shows significant error reductions across multiple architectures.
This paper proposes Fourier Feature Networks (FENs), a single-hidden-layer neural network architecture using Fourier features to solve partial differential equations, achieving higher accuracy than Extreme Learning Machines without affine transformations.
This paper proposes SCORE, a self-concordance-inspired quasi-Newton method for training physics-informed neural networks (PINNs). It uses a decrement-coupled shifted secant geometry to improve final accuracy on nonlinear PDE benchmarks without requiring Hessian computations.
This paper presents a goal-agnostic control framework for partial differential equations using a joint-embedding predictive architecture (JEPA) with a lightweight 2D ViT encoder and action-conditioned latent dynamics, showing that using a learned physical observable probe outperforms raw latent distance for control tasks.
Proposes a hybrid least squares/gradient descent method for MIONets to accelerate training by using alternating least squares for the last layer parameters of multiple branch networks, leveraging Kronecker and Khatri-Rao products.
This paper presents MCO-PDE, a competitive optimization framework that discovers shared partial differential equations from multiple observational datasets by combining neural surrogates, soft-competitive weighting, and genetic algorithms for structure search. It demonstrates high accuracy in recovering canonical equations from limited data and handles complex geometries and real-world experiments.
This paper studies transfer specificity in implicit neural representations across SIREN, ReLU MLPs, and Fourier-feature MLPs, finding that transfer magnitude and specificity depend on architecture, with ReLU being more selective and SIREN reusing weights broadly. Results suggest architecture selection should consider explicit control conditions, not just transfer magnitude.
This paper establishes an exact correspondence between neural network training and Hamilton-Jacobi initial-value problems, unifying deep learning architectures through a deformation parameter.
The paper introduces beignet, a PINN architecture that replaces random Fourier features with a trainable multi-resolution Fourier feature pyramid, achieving higher accuracy and computational efficiency on PDE benchmarks.
This paper introduces breakeven complexity, a metric to determine when neural PDE solvers become cost-effective compared to traditional numerical solvers. The framework uses scaling laws to allocate training budgets and evaluates multiple neural solvers on diverse PDE benchmarks.
This paper proposes a spatially correlated curriculum learning framework for Physics-Informed Neural Networks (PINNs) that improves training stability and solution accuracy by leveraging spatial correlations among subregions, addressing issues like high-dimensional non-convex loss landscapes and imbalanced multi-objective constraints.
This paper extends Port-Hamiltonian Neural Networks (PHNNs) to partial differential equations (PDEs) for learning nonlinear string dynamics from data. The approach recovers both the Hamiltonian and dissipation, outperforming non-physics-informed baselines in accuracy and interpretability.