Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. In high ...

Partial differential equations can describe everything from planetary motion to plate tectonics, but they’re notoriously hard to solve. Unless you’re a physicist or an engineer, there really isn’t ...

SIAM Journal on Numerical Analysis, Vol. 27, No. 3 (Jun., 1990), pp. 704-735 (32 pages) Ordinary differential equations can be recast into a nonlinear canonical form called an S-system. Evidence for ...

Here at VCF, we stumbled across a gigantic contraption that spanned several tables. Rube Goldberg machine this was not. Instead, this device actually does something useful! [Tim Robinson’s] ...

Luis Caffarelli has won the 2023 Abel prize, unofficially called the Nobel prize for mathematics, for his work on a class of equations that describe many real-world physical systems, from melting ice ...

We design a numerical scheme for solving a Dynamic Programming equation with Malliavin weights arising from the time-discretization of backward stochastic differential equations with the integration ...