SPIDeC methods achieve arbitrarily high-order accuracy for positive dynamical systems while unconditionally preserving positivity and equilibria via a multiplicative Volterra structure, and they are L-stable with asymptotic logarithmic contractivity under Gauss-Radau nodes.
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A JAX-based differentiable model of pressure vacuum swing adsorption accelerates cyclic steady-state simulation by 20x via Newton iteration and produces a better Pareto front with IPOPT than NSGA-II in two orders of magnitude less time on a post-combustion capture benchmark.
OTP-FM extends conditional flow matching by incorporating dynamic optimal transport potentials to enable efficient multimarginal transport learning with intermediate observed marginals.
A linear BDF2 finite-element integrator for the LLG equation achieves first-order spatial and second-order temporal convergence rates and converges to both weak and strong solutions.
Spectral Deferred Correction methods achieve at least order p after p iterations when viewed as Runge-Kutta methods, with order jumps of two possible for collocation methods using specific implicit error discretizations.
RedEigCD enables stable timestep increases up to 40 times larger than full-order models for projection-based ROMs of incompressible flows by using exact spectral bounds on reduced convective and diffusive operators together with a proof that ROM stable timesteps are at least as large as FOM ones.
Fully implicit resolvent discretization of noisy accelerated gradient dynamics produces a Lyapunov mean-square recursion whose contraction factor improves and stationary error scales as O(1/α), vanishing for large α under accurate inner solves.
ANTIC reduces storage for large-scale PDE simulations by orders of magnitude through adaptive temporal snapshot selection combined with continual neural-field residual compression while preserving physics accuracy.
An automated Python simulator, calibrated to one experimental run, generates consistent time-series data for many batch distillation scenarios including anomalies, forming an openly released hybrid dataset for deep anomaly detection.
Proof of optimal H1-norm error estimates for A-stable BDF1/BDF2 full discretizations of Willmore flow using surface finite elements of degree at least 2.
Parallel SDC with optimal coefficients solves index-1 DAEs faster than sequential SDC while retaining high accuracy in small-scale parallelism.
A hybrid iterative-sequential method identifies linear DAE systems from errors-in-variables data by partial lagged-data stacking and iterative diagonal error-covariance estimation.
Benchmarking reveals that a numerical escape criterion in hot Jupiter chemical kinetics solvers causes artificial quenching overestimating HCN, CH4, and NH3 by factors of 1.5-3, with remaining discrepancies traced to specific reaction rates and absent species.
Low-rank structure in HBVM stage equations is exploited via Krylov projection for linear cases and Newton-Krylov with adaptive time-stepping for nonlinear cases, shown efficient on semi-discretized wave equations.
GPU port of entropy-stable DG Euler solver with non-conservative buoyancy terms reaches nearly 70% of 64-bit peak on A100 volume kernels, delivers 10x speedup and 13x better energy efficiency versus CPU, and preserves symmetry-based flux savings.
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Stable self-adaptive timestepping for Reduced Order Models for incompressible flows
RedEigCD enables stable timestep increases up to 40 times larger than full-order models for projection-based ROMs of incompressible flows by using exact spectral bounds on reduced convective and diffusive operators together with a proof that ROM stable timesteps are at least as large as FOM ones.
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Low-Rank Solvers for Energy-Conserving Hamiltonian Boundary Value Methods
Low-rank structure in HBVM stage equations is exploited via Krylov projection for linear cases and Newton-Krylov with adaptive time-stepping for nonlinear cases, shown efficient on semi-discretized wave equations.