LiL-Q applies quasilinearization to nonlinear PDEs and solves each resulting linear problem by convex least-squares collocation on Linear-in-Learnables trial spaces, achieving fast convergence and high accuracy on multiple benchmarks.
Gradient-enhanced physics- informed neural networks for forward and inverse PDE problems.Computer Methods in Applied Mechanics and Engineering, 393:114823, 2022
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PI-MFA optimizes tensor-product B-spline control points to balance data fidelity against PDE residuals, producing physically consistent continuous flow fields.
Oscillatory state-space models with PDE-aware spectral bases are introduced as inductive biases for PINNs, yielding improved accuracy and lower memory on forward, inverse, and up to 100D PDE tasks.
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.
LEIA is a world model for autoregressive 3D simulation of architected materials under interactive loading, benchmarked on MicroPlate and applied to surrogate-guided de novo design search with finite-element validation.
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A Physics-Informed B-Spline Framework for Continuous Approximation of Flow Data
PI-MFA optimizes tensor-product B-spline control points to balance data fidelity against PDE residuals, producing physically consistent continuous flow fields.