A weighted FOSLS formulation for deep neural networks solves transmission problems robustly, with proofs that the loss aligns with the energy norm independently of material contrast and shows passive variance reduction.
Gradient-annihilated pinns for solving riemannproblems:Applicationtorelativistichydrodynamics
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vsOED uses a variational one-point reward and RL policy optimization to provide a lower bound on expected information gain for sequential experimental design, supporting nuisance parameters, implicit likelihoods, and multiple design goals.
A WLaSDI-based framework creates noise-robust latent surrogates for PDE-constrained optimization, deriving direct and adjoint gradients to achieve up to five orders of magnitude speedup on radiative transfer, Vlasov-Poisson, and Burgers benchmarks.
A variational neural network using Kolosov-Muskhelishvili potentials solves 2D linear elasticity and fracture problems by minimizing total potential energy and embedding crack discontinuities into the ansatz, yielding higher accuracy and faster convergence than standard physics-informed networks.
Curvature-aware optimizers such as natural gradient and self-scaling BFGS/Broyden accelerate PINN convergence and accuracy on PDEs including Helmholtz, Stokes, Burgers, and Euler equations plus stiff ODEs, with new model formulations and batched scaling.
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Robust Deep FOSLS for Transmission Problems
A weighted FOSLS formulation for deep neural networks solves transmission problems robustly, with proofs that the loss aligns with the energy norm independently of material contrast and shows passive variance reduction.
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Curvature-Aware Optimization for High-Accuracy Physics-Informed Neural Networks
Curvature-aware optimizers such as natural gradient and self-scaling BFGS/Broyden accelerate PINN convergence and accuracy on PDEs including Helmholtz, Stokes, Burgers, and Euler equations plus stiff ODEs, with new model formulations and batched scaling.