Fast training of accurate physics-informed neural networks without gradient descent

Solving time-dependent Partial Differential Equations (PDEs) is one of the most critical problems in computational science. While Physics-Informed Neural Networks (PINNs) offer a promising framework for approximating PDE solutions, their accuracy and training speed are limited by two core barriers: gradient-descentbased iterative optimization over complex loss landscapes and non-causal treatment of time as an extra spatial dimension. We present Frozen-PINN, a novel PINN based on the principle of space-time separation that leverages random features instead of training with gradient descent, and incorporates temporal causality by construction. On nine PDE benchmarks, including challenges like extreme advection speeds, shocks, and high-dimensionality, Frozen-PINNs achieve superior training efficiency and accuracy over state-of-the-art PINNs, often by several orders of magnitude. Our work addresses longstanding training and accuracy bottlenecks of PINNs, delivering quickly trainable, highly accurate, and inherently causal PDE solvers, a combination that prior methods could not realize. Our approach challenges the reliance of PINNs on stochastic gradient-descent-based methods and specialized hardware, leading to a paradigm shift in PINN training and providing a challenging benchmark for the community. INTRODUCTION Partial Differential Equations (PDEs) provide a unifying framework for modeling complex dynamical systems across physics, biology, and engineering, yet developing efficient methods to solve them remains a longstanding challenge (Farlow, 1993) . Deep neural networks have recently shown significant promise for approximating solutions of PDEs because of the mesh-free construction of basis functions, high expressivity of neural networks (Rudi & Rosasco, 2021), their ability to represent functions in high dimensions (E