‘Optical neural engine’ can solve partial differential equations
Partial differential equations (PDEs) are a class of mathematical problems that represent the interplay of multiple variables, and therefore have predictive power when it comes to complex physical systems. Solving these equations is a perpetual challenge, however, and current computational techniques for doing so are time-consuming and expensive.
This paper introduces a novel generative modeling framework grounded in phase space dynamics, taking inspiration from the principles underlying Critically Damped Langevin Dynamics (CLD). Leveraging insights from stochastic optimal control, we construct a favorable path measure in the phase space that proves highly advantageous for generative sampling. A distinctive feature…
Behrooz Tahmasebi—an MIT Ph.D. student in the Department of Electrical Engineering and Computer Science (EECS) and an affiliate of the Computer Science and Artificial Intelligence Laboratory (CSAIL)—was taking a mathematics course on differential equations in late 2021 when a glimmer of inspiration struck. In that class, he learned for the…
For more than 250 years, mathematicians have wondered if the Euler equations might sometimes fail to describe a fluid’s flow. Now there’s a breakthrough.