The fdaPDE core library is a C++ header-only library for Partial Differential Equation discretization, computational geometry, unconstrained nonlinear optimization, linear algebra and much more.

Scientific machine learning (SciML) benchmarks, AI for science, and (differential) equation solvers. Covers Julia, Python (PyTorch, Jax), MATLAB, R ...

(Courtesy: R.G. MacDonald, A. Yakovlev, and V. Pacheco-Peña, doi : 10.1117/1.APN.3.5.056007) Waveguide-based structures can solve partial differential equations by mimicking elements in standard ...

"It can work basically on any problem, in any domain of science or engineering, to solve partial differential equations on ...

The course gives an introduction to analytical techniques for partial differential equations, in particular to separation of variables. In addition the course treats qualititative properties of ...

We study the classical linear partial differential equations: Poisson's equation and the heat equation. We learn about representation formulas for solutions, maximum principles, and energy estimates.

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A new artificial intelligence (AI) system could make solving complex engineering problems thousands of times faster, even on ...

The new AI significantly speeds up heart disease predictions, reducing calculation time from hours to 30 seconds. It can be ...