From the 1 of 5 linked papers with an AI index.
5 papers
Exact Total Variation Minimizers as Non-Oscillatory Limiters in High-Order Methods for Conservation Laws
Gabriel P. Langlois, Jerome Darbon, Rongjie Lai +2
The paper introduces a post‑processing step that applies exact total‑variation denoising, computed via a differential inclusion algorithm, to eliminate spurious oscillations in hig…
Spectrally Safe Neural Operator Warm-Starts for Large-Scale Newton Solvers
Jaemin Oh, Youngkyu Lee, Jerome Darbon +1
Neural operators are increasingly used to warm-start Newton solvers for nonlinear PDEs, on the premise that a low test error places the initial guess inside the basin of attraction…
PI-SONet: A Physics-Informed Symplectic Operator Network for Real-Time Optimal Control of Multi-Agent Systems
Alan John Varghese, Shanqing Liu, Paula Chen +3
Many real-life applications involve controlling high-dimensional multi-agent systems in real-time. Existing optimal control solvers often suffer from the curse-of-dimensionality an…
PINNs in PDE Constrained Optimal Control Problems: Direct vs Indirect Methods
Zhen Zhang, Shanqing Liu, Alessandro Alla +2
We study physics-informed neural networks (PINNs) as numerical tools for the optimal control of semilinear partial differential equations. We first recall the classical direct and…
A fast algorithm for solving the lasso problem exactly without homotopy using differential inclusions
Gabriel P. Langlois, Jérôme Darbon
We prove in this work that the well-known lasso problem can be solved exactly without homotopy using novel differential inclusions techniques. Specifically, we show that a selectio…