94 citations · 785 across the 34 of their papers we have counts for
5 papers · 1 filter
Complex networks with complex weights
Lucas Böttcher, Mason A. Porter
In many studies, it is common to use binary (i.e., unweighted) edges to examine networks of entities that are either adjacent or not adjacent. Researchers have generalized such bin…
Visualizing high-dimensional loss landscapes with Hessian directions
Lucas Böttcher, Gregory Wheeler
Analyzing geometric properties of high-dimensional loss functions, such as local curvature and the existence of other optima around a certain point in loss space, can help provide…
Near-optimal control of dynamical systems with neural ordinary differential equations
Lucas Böttcher, Thomas Asikis
Optimal control problems naturally arise in many scientific applications where one wishes to steer a dynamical system from a certain initial state to a desired targe…
Spectrally Adapted Physics-Informed Neural Networks for Solving Unbounded Domain Problems
Mingtao Xia, Lucas Böttcher, Tom Chou
Solving analytically intractable partial differential equations (PDEs) that involve at least one variable defined on an unbounded domain arises in numerous physical applications. A…
Control of Dual-Sourcing Inventory Systems using Recurrent Neural Networks
Lucas Böttcher, Thomas Asikis, Ioannis Fragkos
A key challenge in inventory management is to identify policies that optimally replenish inventory from multiple suppliers. To solve such optimization problems, inventory managers…