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.
DGM: A deep learning algorithm for solving partial differential equations , volume=
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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.
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.
citing papers explorer
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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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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.