Discovering Global Minima of High-Dimensional Energy Landscapes
Keywords: non-convex optimization, structural biology, statistical mechanics
TL;DR: We propose a novel neural network loss that allows us to recover the global minima of high-dimensional, non-convex functions.
Abstract: Identifying global minima of high-dimensional non-convex functions is a fundamental problem in fields such as structural biology and materials modeling. Existing solutions (e.g. AlphaFold) often rely on generalizing from data. In contrast, we address the challenging domain where no existing data is available, and only the ground-truth energy function is provided. Utilizing the action functional, we formulate a novel loss function that transforms the input's rough loss landscape into a benign one for the neural network parameters. This allows minimizing the loss to align with finding the global minimum of the energy landscape. We validate our method on high-dimensional global optimization tasks, demonstrating its ability to approximate global minima for energy landscapes with thousand-dimensional inputs.
Supplementary Material: zip
Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)
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Submission Number: 12131
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