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⚡️New research on probabilistic numerical solvers for (partial) differential equations ⚡️
How do I solve nonlinear, time-dependent #pde's with a #probnum algorithm?
A thread. (1/7)
How do I solve nonlinear, time-dependent #pde's with a #probnum algorithm?
A thread. (1/7)
How do you solve a time-dependent PDE efficiently without probabilistic numerics? 🧐 Many will probably answer with the method of lines: discretise the differential equation in space, and use an ODE solver for the rest. ✔️ (2/7)
But this is a pipeline of TWO solvers, not one solver 🤯 What happens if the space-discretisation is bad, but the ODE solver uses high precision, i.e., low absolute and relative tolerances? Computation is wasted, and ODE-solver uncertainty quantification becomes useless 😭 (3/7)
