In pure mathematics, ChatGPT-5.4 was credited with aiding the solution of a notoriously difficult Erdős problem, a feat that had eluded experts for decades. In applied mathematics, University of ...
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Penn engineers use AI to solve some of science's most difficult math problems
A ripple tells you something happened, but not exactly what. That is the core problem behind a hard class of equations that ...
Penn Engineers have developed a new way to use AI to solve inverse partial differential equations (PDEs), a particularly ...
Accompanying code for NeurIPS 2020 paper (Poster). Deep Learning based algorithm for solving a parametrized family of high-dimensional Kolmogorov PDEs. Implemented in PyTorch and Tune. Black-Scholes ...
Nearly 200 years ago, the physicists Claude-Louis Navier and George Gabriel Stokes put the finishing touches on a set of equations that describe how fluids swirl. And for nearly 200 years, the ...
Adequate mathematical modeling is the key to success for many real-world projects in engineering, medicine, and other applied areas. Once a well-suited model is established, it can be thoroughly ...
Partial Differential Equations (PDEs) are central to both pure and applied mathematics. Any quantity which changes in space and time will satisfy certain partial differential equations because the ...
ABSTRACT: This paper is devoted to numerically solving the Burgers’ equation in unbounded region, which describes the nonlinear wave propagation and diffusion effect. How to numerically and ...
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