Normalizing flows are constructed by learning the velocity of a stochastic interpolant via a quadratic loss derived from its probability current, yielding an efficient ODE-based alternative to diffusion models.
A family of embedded Runge-Kutta formulae
21 Pith papers cite this work. Polarity classification is still indexing.
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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.
The curvature-aware precision controller adapts between FP32 and FP64 during PINN training to match double-precision accuracy at reduced computational cost.
Composed BDF schemes with complex coefficients increase order by one, supply order p+1 error estimates from the imaginary part, break the Dahlquist barrier up to order 8, and give step-ratio stability bounds for non-uniform meshes.
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.
Bi-CFM learns bidirectional mappings between initial and final state distributions to solve ill-posed inverse problems in chaotic systems, reporting metric improvements and speedups on Lorenz variants plus conservation-respecting results on three-body and globular cluster data.
Evolutionary selection on reservoir size, connectivity, spectral radius, input scaling, and regularization for Kuramoto-Sivashinsky forecasting reveals a conserved stochastic-block-model spectral envelope, locked intermediate modularity, and a horizontal cost-modularity floor in elite architectures.
INDEQS is a graph-informed NCDE variant that separates inner hidden-state mixing from outer vector-field mixing and reports lower MAE than uninformed NCDEs on synthetic advection data and real river/traffic tasks when the graph is known.
A beta-VAE analysis of pop-cosmos models finds that five latent dimensions capture the rest-frame optical SED, corresponding to stellar mass, recent star formation, dust, and two gas ionization states.
PIDM-DP integrates Dormand-Prince ODE solving into DDPM denoising with scheduled physics guidance to reconstruct chaotic states, reporting up to 15.4x RMSE gains over baselines on five systems including stiff cases.
SITN performs single-sample OOD detection via goodness-of-fit testing on noise samples in the factorised latent space of continuous normalizing flows.
Nowhere-vanishing Koopman eigenfunctions form a multiplicative group, enabling polynomial extensions from principal ones to enrich eigenspaces and enable global representations from local data in multistable systems.
Galaxy size-mass relations exhibit double power-law breaks at different pivot masses for quiescent versus bulge-dominated samples, coinciding with AGN activity scales.
Flow matching achieves single-step pixel accuracy and 20-step perceptual quality for Sentinel-2 super-resolution, outperforming diffusion and Real-ESRGAN while enabling large-scale 2.5 m land-cover products.
Polytropic stellar wind models are extended beyond extreme adiabatic cases to non-adiabatic localized heating, with added energy shown plausible relative to flares and relevant to solar wind observations.
BG-SINDy reformulates l0-constrained regression as term-level l2,0 regularization and uses progressive pruning guided by balance contributions to recover small-coefficient terms in multiscale PDEs.
Bayesian-ARGOS is a hybrid frequentist-Bayesian method that discovers equations from limited noisy observations more efficiently than SINDy or bootstrap-ARGOS while adding uncertainty quantification.
S-MNN reformulates Mechanistic Neural Networks to achieve linear computational complexity for long sequences while preserving accuracy and interpretability.
The Parker-Sochacki method delivers 4 to 13 orders of magnitude better kinetic energy conservation than Runge-Kutta methods for charged particle motion in static magnetic fields while running faster at matched accuracy.
Experimental imbibition data on four porous materials are pre-processed with a monotonicity-preserving fit and used to calibrate a PDE model of capillary absorption.
citing papers explorer
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Stable Positive Integral Deferred Correction Methods for Positive Dynamical Systems
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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Curvature-aware dynamic precision approach for physics-informed neural networks
The curvature-aware precision controller adapts between FP32 and FP64 during PINN training to match double-precision accuracy at reduced computational cost.
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Error estimation for numerical approximations of ODEs via composition techniques. Part II: BDF methods
Composed BDF schemes with complex coefficients increase order by one, supply order p+1 error estimates from the imaginary part, break the Dahlquist barrier up to order 8, and give step-ratio stability bounds for non-uniform meshes.
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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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Solving Inverse Problems of Chaotic Systems with Bidirectional Conditional Flow Matching
Bi-CFM learns bidirectional mappings between initial and final state distributions to solve ill-posed inverse problems in chaotic systems, reporting metric improvements and speedups on Lorenz variants plus conservation-respecting results on three-body and globular cluster data.
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Evolutionary Optimization Reveals Structural Constraints on Reservoir Architecture for Spatiotemporal Chaos
Evolutionary selection on reservoir size, connectivity, spectral radius, input scaling, and regularization for Kuramoto-Sivashinsky forecasting reveals a conserved stochastic-block-model spectral envelope, locked intermediate modularity, and a horizontal cost-modularity floor in elite architectures.
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INDEQS: Informed Neural controlled Differential EQuationS
INDEQS is a graph-informed NCDE variant that separates inner hidden-state mixing from outer vector-field mixing and reports lower MAE than uninformed NCDEs on synthetic advection data and real river/traffic tasks when the graph is known.
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pop-cosmos: Disentangling galaxy properties from observables using data-driven approaches
A beta-VAE analysis of pop-cosmos models finds that five latent dimensions capture the rest-frame optical SED, corresponding to stellar mass, recent star formation, dust, and two gas ionization states.
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PIDM-DP: Physics-Informed Diffusion with Dormand-Prince Integration for Chaotic System Identification and State Reconstruction across Multiple Dynamical Regimes
PIDM-DP integrates Dormand-Prince ODE solving into DDPM denoising with scheduled physics guidance to reconstruct chaotic states, reporting up to 15.4x RMSE gains over baselines on five systems including stiff cases.
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The Signal in the Noise: OOD Detection Through Goodness-of-Fit Testing in Factorised Latent Spaces
SITN performs single-sample OOD detection via goodness-of-fit testing on noise samples in the factorised latent space of continuous normalizing flows.
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On the algebra of Koopman eigenfunctions and on some of their infinities
Nowhere-vanishing Koopman eigenfunctions form a multiplicative group, enabling polynomial extensions from principal ones to enrich eigenspaces and enable global representations from local data in multistable systems.
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pop-cosmos: Galaxy size evolution across structural and star-formation classifications in COSMOS-Web
Galaxy size-mass relations exhibit double power-law breaks at different pivot masses for quiescent versus bulge-dominated samples, coinciding with AGN activity scales.
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Flow matching for Sentinel-2 super-resolution: implementation, application, and implications
Flow matching achieves single-step pixel accuracy and 20-step perceptual quality for Sentinel-2 super-resolution, outperforming diffusion and Real-ESRGAN while enabling large-scale 2.5 m land-cover products.
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Polytropic stellar wind models with strongly localized heating
Polytropic stellar wind models are extended beyond extreme adiabatic cases to non-adiabatic localized heating, with added energy shown plausible relative to flares and relevant to solar wind observations.
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Balance-Guided Sparse Identification of Multiscale Nonlinear PDEs with Small-coefficient Terms
BG-SINDy reformulates l0-constrained regression as term-level l2,0 regularization and uses progressive pruning guided by balance contributions to recover small-coefficient terms in multiscale PDEs.
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Fast and principled equation discovery from chaos to climate
Bayesian-ARGOS is a hybrid frequentist-Bayesian method that discovers equations from limited noisy observations more efficiently than SINDy or bootstrap-ARGOS while adding uncertainty quantification.
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Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning
S-MNN reformulates Mechanistic Neural Networks to achieve linear computational complexity for long sequences while preserving accuracy and interpretability.
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High-Accuracy Numerical Solutions of Particle Motion in Static Magnetic Fields
The Parker-Sochacki method delivers 4 to 13 orders of magnitude better kinetic energy conservation than Runge-Kutta methods for charged particle motion in static magnetic fields while running faster at matched accuracy.
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Data-Informed Mathematical Characterization of Absorption Properties in Artificial and Natural Porous Materials
Experimental imbibition data on four porous materials are pre-processed with a monotonicity-preserving fit and used to calibrate a PDE model of capillary absorption.