A multihead PINN with orthogonalized linear heads learns low-dimensional latent embeddings of PDE solution families, with 2–4 principal components capturing 95% of latent variance for Burgers, heat, and wave equations.
Journal of Computational Physics 375:1339--1364
10 Pith papers cite this work, alongside 2,125 external citations. Polarity classification is still indexing.
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A PINN framework with separate networks for conductivity and potentials, multiscale wavelet excitations, and FFE recovers dominant conductivity structures from finite DtN data with 3-12% relative error on synthetic tests, with FFE aiding sharp features.
NPSolver trains neural Poisson solvers label-free by supervising with a small number of preconditioned conjugate gradient steps and adds Boundary-Aware Transolver for mixed boundaries, outperforming baselines on 2D/3D irregular geometries.
A framework that structurally enforces divergence-free velocity and long-range transport coherence in 3D fluid reconstruction from 2D videos via divergence-free kernels advecting Lagrangian Gaussian splats.
A specialized PINN architecture solves the spatially inhomogeneous electron Boltzmann equation with high accuracy across gases and electric field strengths without case-specific tuning.
Deep-Picard iteration uses supervised neural networks trained on Monte Carlo labels from beta-stable subordinators and alpha-stable Levy walks to approximate solutions of high-dimensional fractional PDEs up to dimension 100.
An adaptive anisotropic composite quadrature strategy combined with refresh-based training narrows the gap between training and reference losses in neural residual minimization for PDEs while using quadrature points more efficiently.
Proposes an unbiased, second-order-free training framework for BSDE solvers of high-dimensional PDEs that corrects Euler-Maruyama discretization bias while preserving computational advantages.
Causal PDE-Control Models combine causal drivers with PDE control and filtering to deliver interpretable dynamic portfolio rules that outperform benchmarks in Sharpe ratio and turnover on U.S. equity data.
Introduces Laplace-approximated Bayesian PINNs for automatic loss-weight optimization when solving PDEs such as heat, wave, and Burgers equations.
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Physics-Informed Neural Embeddings of PDE Solution Families
A multihead PINN with orthogonalized linear heads learns low-dimensional latent embeddings of PDE solution families, with 2–4 principal components capturing 95% of latent variance for Burgers, heat, and wave equations.
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Recovering Sharp Conductivity Features in the Finite-Data Calder\'on Problem with Physics-Informed Neural Networks
A PINN framework with separate networks for conductivity and potentials, multiscale wavelet excitations, and FFE recovers dominant conductivity structures from finite DtN data with 3-12% relative error on synthetic tests, with FFE aiding sharp features.
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NPSolver: Neural Poisson Solver with Iterative Physics Supervision
NPSolver trains neural Poisson solvers label-free by supervising with a small number of preconditioned conjugate gradient steps and adds Boundary-Aware Transolver for mixed boundaries, outperforming baselines on 2D/3D irregular geometries.
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LagrangianSplats: Divergence-Free Transport of Gaussian Primitives for Fluid Reconstruction
A framework that structurally enforces divergence-free velocity and long-range transport coherence in 3D fluid reconstruction from 2D videos via divergence-free kernels advecting Lagrangian Gaussian splats.
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A physics-informed neural network approach to solve the spatially inhomogeneous electron Boltzmann equation
A specialized PINN architecture solves the spatially inhomogeneous electron Boltzmann equation with high accuracy across gases and electric field strengths without case-specific tuning.
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Deep-Picard Iteration for Space-time Fractional Diffusion PDEs
Deep-Picard iteration uses supervised neural networks trained on Monte Carlo labels from beta-stable subordinators and alpha-stable Levy walks to approximate solutions of high-dimensional fractional PDEs up to dimension 100.
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Adaptive anisotropic composite quadratures for residual minimisation in neural PDE approximations
An adaptive anisotropic composite quadrature strategy combined with refresh-based training narrows the gap between training and reference losses in neural residual minimization for PDEs while using quadrature points more efficiently.
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Unbiased and Second-Order-Free Training for High-Dimensional PDEs
Proposes an unbiased, second-order-free training framework for BSDE solvers of high-dimensional PDEs that corrects Euler-Maruyama discretization bias while preserving computational advantages.
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Causal PDE-Control Models for Dynamic Portfolio Optimization with Latent Drivers
Causal PDE-Control Models combine causal drivers with PDE control and filtering to deliver interpretable dynamic portfolio rules that outperform benchmarks in Sharpe ratio and turnover on U.S. equity data.
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Bayesian Reasoning for Physics Informed Neural Networks
Introduces Laplace-approximated Bayesian PINNs for automatic loss-weight optimization when solving PDEs such as heat, wave, and Burgers equations.