8 papers
A Transformer-based Approach for Real-time Multi-agent Path Planning with Varying Initial/Final Conditions
Qian Zhang, Shanqing Liu, Jerome Darbon +1
We address the problem of real-time multi-agent path planning under prescribed initial and final configurations, formulated as a high-dimensional optimal control problem subject to…
Continuous-time analysis and algorithms for linear and convex quadratic programs via exactly solvable differential inclusions
Gabriel P. Langlois, Akwum Onwunta, Jérôme Darbon
Linear and convex quadratic programs are fundamental problems in optimization. While many methods have been developed for solving these programs in large-scale applications, to our…
Exact Total Variation Minimizers as Non-Oscillatory Limiters in High-Order Methods for Conservation Laws
Gabriel P. Langlois, Jerome Darbon, Rongjie Lai +2
High-order numerical methods for conservation laws can generate spurious oscillations near discontinuities. We propose to suppress these oscillations by post-processing the numeric…
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…
Efficient first-order algorithms for large-scale, non-smooth maximum entropy models with application to wildfire science
Gabriel P. Langlois, Jatan Buch, Jérôme Darbon
Maximum entropy (Maxent) models are a class of statistical models that use the maximum entropy principle to estimate probability distributions from data. Due to the size of modern…