Kernmechanica

Kernmechanica is an emerging interdisciplinary framework that applies kernel methods from machine learning to problems in mechanics, including classical, quantum, and statistical mechanics. Proponents describe it as a data-driven approach to model and analyze the evolution of physical systems without assuming explicit parametric equations.

The core toolset centers on reproducing-kernel Hilbert spaces and positive-definite kernels to construct nonparametric representations of states, energies, and dynamical operators. Kernels enable flexible function estimation and the embedding of state spaces into high-dimensional feature spaces. In kernmechanica, dynamical evolution is often represented through kernelized operators such as the Koopman or Liouville operators, or through learned Hamiltonian/Lagrangian surrogates that respect physical constraints.

Common methods include kernel regression and Gaussian process dynamical models for state forecasting, kernelized differential equations (KODEs), and kernelized dynamic mode decomposition. Techniques emphasize regularization, uncertainty quantification, and preservation of structural properties like conservation laws or symplectic structure where possible.

Applications span robotics and control, molecular and materials simulation, fluid and plasma dynamics, and astrophysical systems, especially where data are abundant but governing equations are complex or partially unknown.

The term kernmechanica appears in recent literature and conference discussions as an umbrella for data-driven mechanics approaches. It is not universally adopted and remains a developing field, with ongoing work addressing interpretability, physical validity, and scalable computation.