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Expand file tree Collapse file tree Original file line number Diff line number Diff line change @@ -132,6 +132,27 @@ Stochastic differential equations integrate over many sample paths with
132132jmax sde " 0.05*y" " 0.2*y" --y0 1 --t1 1 --paths 4000 --plot path.svg
133133```
134134
135+ Ordinary differential equations are solved with ` jmax ode ` ; ` --method rosenbrock `
136+ selects an L-stable stiff solver, and ` --events "<g>" ` reports zero-crossings:
137+
138+ ``` bash
139+ jmax ode " -1000*(y - cos(t)) - sin(t)" 1 --tf 1 --method rosenbrock # stiff -> cos(t)
140+ ```
141+
142+ ## Machine learning for operators
143+
144+ ` jmax fno ` demonstrates a Fourier Neural Operator learning a solution * operator*
145+ from example fields (differentiation, integration, or smoothing) rather than a
146+ fixed input/output pair:
147+
148+ ``` bash
149+ jmax fno --operator deriv --plot fno.svg # learns differentiation to ~1e-15
150+ jmax fno --operator smooth # learns a Gaussian-smoothing operator
151+ ```
152+
153+ The spectral convolution (FFT, per-mode complex weights, inverse FFT) and the
154+ operator fit are pure Rust; this is the building block for PDE surrogate models.
155+
135156## Symbolic algebra
136157
137158JMax carries a computer algebra system. From ` jmax eval ` , expressions with free
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