PRISM enables zero-shot parameterized high-dimensional high-order neural PDE solvers via implicit stochastic modulation that decouples parameters from the differentiation graph while preserving unbiased estimators.
Gradient-annihilated pinns for solving riemannproblems:Applicationtorelativistichydrodynamics
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A variational physics-informed neural network using Kolosov-Muskhelishvili potentials is introduced for 2D linear elasticity and fracture problems, embedding crack conditions directly into the ansatz.
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.
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.
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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Time-Dependent PDE-Constrained Optimization via Weak-Form Latent Dynamics
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.