Compression of Polyconvex Envelopes of Isotropic Functions via Monotonic Input Convex Neural Networks

What the math gives to ML

The transferable asset is a constructive sufficient condition for polyconvexity: represent an isotropic energy through its positive singular values and enforce convexity plus coordinatewise monotonicity with nonnegative-weight ICNNs. This turns a difficult envelope-computation problem into constrained regression in a reduced-dimensional invariant space, while the envelope property can be enforced by training the learned energy from below. The same pattern can provide stable energy surrogates for differentiable simulation, inverse mechanics, and neural constitutive laws, although the guarantee is sufficient rather than necessary and finite-sample penalties must be validated.