arXiv subjects

Todd Munson

Publications and source records attributed to Todd Munson.

21 records · Page 2Linked to original sources

arXiv2020

Training neural networks under physical constraints using a stochastic augmented Lagrangian approach

We investigate the physics-constrained training of an encoder-decoder neural network for approximating the Fokker-Planck-Landau collision operator in the 5-dimensional kinetic fusion simulation in XGC. To train this network, we propose a stochastic augmented Lagrangian approach that utilizes pyTorch's native stochastic gradient descent method to solve the inner unconstrained minimization subproblem, paired with a heuristic update for the penalty factor and Lagrange multipliers in the outer augmented Lagrangian loop. Our training results for a single ion species case, with self-collisions and collision against electrons, show that the proposed stochastic augmented Lagrangian approach can achieve higher model prediction accuracy than training with a fixed penalty method for our application problem, with the accuracy high enough for practical applications in kinetic simulations.

physics.comp-ph↗

arXiv2017

Platoon formation maximization through centralized routing and departure time coordination

Platooning allows vehicles to travel with small intervehicle distance in a coordinated fashion thanks to vehicle-to-vehicle connectivity. When applied at a larger scale, platooning will create significant opportunities for energy savings due to reduced aerodynamic drag, as well as increased road capacity and congestion reduction resulting from shorter vehicle headways. However, these potential savings are maximized if platooning-capable vehicles spend most of their travel time within platoons. Ad hoc platoon formation may not ensure a high rate of platoon driving. In this paper we consider the problem of central coordination of platooning-capable vehicles. By coordinating their routes and departure times, we can maximize the fuel savings afforded by platooning vehicles. The resulting problem is a combinatorial optimization problem that considers the platoon coordination and vehicle routing problems simultaneously. We demonstrate our methodology by evaluating the benefits of a coordinated solution and comparing it with the uncoordinated case when platoons form only in an ad hoc manner. We compare the coordinated and uncoordinated scenarios on a grid network with different assumptions about demand and the time vehicles are willing to wait.

eess.SY↗

arXiv2015

A Two-Level Approach to Large Mixed-Integer Programs with Application to Cogeneration in Energy-Efficient Buildings

We study a two-stage mixed-integer linear program (MILP) with more than 1 million binary variables in the second stage. We develop a two-level approach by constructing a semi-coarse model (coarsened with respect to variables) and a coarse model (coarsened with respect to both variables and constraints). We coarsen binary variables by selecting a small number of pre-specified daily on/off profiles. We aggregate constraints by partitioning them into groups and summing over each group. With an appropriate choice of coarsened profiles, the semi-coarse model is guaranteed to find a feasible solution of the original problem and hence provides an upper bound on the optimal solution. We show that solving a sequence of coarse models converges to the same upper bound with proven finite steps. This is achieved by adding violated constraints to coarse models until all constraints in the semi-coarse model are satisfied. We demonstrate the effectiveness of our approach in cogeneration for buildings. The coarsened models allow us to obtain good approximate solutions at a fraction of the time required by solving the original problem. Extensive numerical experiments show that the two-level approach scales to large problems that are beyond the capacity of state-of-the-art commercial MILP solvers.

math.OC↗