Category-theoretic functorial invariants built from directed path algebras on templexes yield separable homology and semigroup structures that detect chaos and tipping points from data.
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GQPINNs add symmetry awareness to quantum PINNs via equivariant circuits, yielding lower mean absolute error and fewer parameters than standard QPINNs on linear and nonlinear PDE benchmarks.
DC-PINNs embed derivative constraints into PINN optimization using a minimum principle and adaptive balancing, reducing violations and improving fidelity on heat, finance, and fluid benchmarks.
A review summarizing machine learning methods for multi-messenger probes of dark matter and new physics, with a proposed plan for future integrated analyses.
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Geometric Quantum Physics Informed Neural Network
GQPINNs add symmetry awareness to quantum PINNs via equivariant circuits, yielding lower mean absolute error and fewer parameters than standard QPINNs on linear and nonlinear PDE benchmarks.