Characterization of blowup for reduced models of Euler equations, see [Blowup Analysis for a Quasi-exact 1D Model of 3D Euler and Navier-Stokes].
Numerical investigation of blowup profiles using dynamic rescaling equations and neural networks, see [Fourier Continuation for Exact Derivative Computation in Physics-Informed Neural Operators].
Computer-assisted proofs for problems of blowup and constructed profiles.
Model reduction and homogenization techinques in multiscale equation, see [Exponential Convergence for Multiscale Linear Elliptic PDEs via Adaptive Edge Basis Functions], [Exponentially Convergent Multiscale Methods for 2D High Frequency Heterogeneous Helmholtz Equations].
See also the review paper [Exponentially Convergent Multiscale Finite Element Method].
Hermite Spectral Method as equilibrium-preserving techniques for kinetic equations, see [Approximation to Singular Quadratic Collision Model in Fokker-Planck-Landau Equation].
Convergence and stability of nonlinear numerical schemes for kinetic equations.
Ensemble sampling method for inverse problems based on underdamped Langevin equation, see [Second Order Ensemble Langevin Method for Sampling and Inverse Problems].
Reduced approximation model for principal-component analysis based on operator approximation via the Schrödinger equation, see [Schrödinger Principal-component Analysis: On the Duality between Principal-component Analysis and the Schrödinger Equation].