arXiv Machine Learning
Learning Implicit Solves for Dynamic Simulations
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arXiv Machine Learning
Jun 16
ANCHOR: Error-Controlled Adaptive Numerical Correction for Neural Operator Time Marching
arXiv:2512. 19643v2 Announce Type: replace Abstract: Numerical simulation of time-dependent partial differential equations (PDEs) is central to scientific and engineering applications, but high-fidelity solvers are often prohibitively expensive for long-horizon or time-critical settings.
arXiv Machine Learning
Jul 21
One-shot acceleration of transient PDE solvers via online-learned preconditioners
arXiv:2509. 08765v4 Announce Type: replace-cross Abstract: Data-driven acceleration of scientific computing workflows has been a high-profile aim of machine learning (ML) for science, with numerical simulation of transient partial differential equations (PDEs) being one of the main applications.
arXiv Machine Learning
Jun 3
Flow Learners for PDEs: Toward a Physics-to-Physics Paradigm for Scientific Computing
arXiv:2604. 07366v2 Announce Type: replace Abstract: Partial differential equations (PDEs) govern nearly every physical process in science and engineering, but solving them at scale remains prohibitively expensive.
arXiv Machine Learning
Aug 14
Physics-Informed Laplace Neural Operator for Solving Partial Differential Equations
arXiv:2602. 12706v2 Announce Type: replace Abstract: Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs).
arXiv AI
Aug 25
One-Step Evolution for Long-Time Extrapolation: An Error-Bound-Informed and Prior-Guided Neural Residual Framework for Autonomous PDEs
arXiv:2608.22026v1 Announce Type: new Abstract: Accurate simulation of the long-time evolution of systems governed by partial differential equations (PDEs) is central to scientific computing. Among e...
arXiv Machine Learning
Sep 4
Time Without Timesteps: Simulating Coupled Dynamical Systems via Self-Consistency
The paper introduces a new method for simulating coupled dynamical systems that bypasses traditional time‑stepping. Instead of marching through time, each subsystem is represented by a neural surrogate that maps an entire driving trajectory and initial condition to a full output trajectory. Coupling is achieved by enforcing self‑consistency across these trajectories, turning the simulation into a fixed‑point problem over complete trajectories. Experiments on van der Pol oscillators and Hodgkin‑Huxley neuron networks show that only 4–10 Newton iterations are needed, compared to 1500 steps for a conventional integrator, and that the gradient can be computed without time recursion using GMRES. The spectral radius of the surrogate’s Jacobian predicts convergence, and the implicit gradient remains accurate even when unrolled backpropagation diverges.