A practical input-to-state stability certificate for Koopman learning control is derived, separating prediction residuals from selected-channel margins and projection residuals.
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Proceedings of the National Academy of Sciences 17, 315–318
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Deep-Koopman-KANDy recovers symbolic Koopman dictionaries post-training by replacing the encoder and decoder with KANs and applying a level-set construction with chain-rule gradients, achieving high recall on Lorenz and expected behavior on other maps.
A novel identity connects reduced-model drift and diffusion to the conditional score of the finite-time transition density, turning calibration into a least-squares problem over stationary lagged pairs that preserves invariant statistics and dynamical correlations.
Koopman autoencoders with forcings and temporal unrolling deliver accurate year-long predictions for coastal-ocean models at 300-1400x speedup, outperforming POD in two of three cases.
Physiome-ODE is a new benchmark consisting of 50 IMTS datasets derived from biological ODEs that shows ODE-based forecasting models performing better and differentiating more meaningfully than on the existing four datasets.
Constructs crossed-product von Neumann algebras M_u from incompressible flows to define commutator-based tracial complexity functionals linked to determinants and entropy.
A tensor train method computes the Koopman generator via operator logarithm while preserving low-rank structure for scalable identification of high-dimensional nonlinear dynamics.
Koopman autoencoders with attention-free latent memory and online change-point re-encoding reduce long-horizon error on Duffing, Repressilator, and IRMA benchmarks while keeping low latency.
Classical probabilistic transport equations are reformulated as quantum systems whose wave function obeys Schrödinger evolution and whose observables include non-commuting operators for statistical quantities.
A non-intrusive framework combines Koopman autoencoders with a spatio-temporal surrogate to learn and predict physics-constrained dynamics of systems like 2D flow around a cylinder for unseen conditions.
The Dirac equation emerged from multiple simultaneous contributions in 1928, with Kramers' independent work and modern derivations from Ehrenfest relations and hydrodynamics now detailed.
DATO and QMDA represent substantially different assimilation paradigms with distinct advantages and limitations in interpretability, robustness, and scalability.
Nelson's stochastic mechanics supplies a configuration-space diffusion picture where the Born rule is built-in, collapse is not an extra axiom, and nonlocality is softened, while proposing a distance scale to test limits of Bell correlations.
The note argues that the classical N-particle distribution equals the diagonal of the density matrix operator in coordinate representation and derives a generalized BBGKY hierarchy for reduced density matrices.
citing papers explorer
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Input-to-State Stability Certification via Projection Residuals for Koopman Learning Control of Nonlinear Repetitive Systems
A practical input-to-state stability certificate for Koopman learning control is derived, separating prediction residuals from selected-channel margins and projection residuals.
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Deep-Koopman-KANDy: Dictionary Discovery for Deep-Koopman Operators with Kolmogorov-Arnold Networks for Dynamics
Deep-Koopman-KANDy recovers symbolic Koopman dictionaries post-training by replacing the encoder and decoder with KANs and applying a level-set construction with chain-rule gradients, achieving high recall on Lorenz and expected behavior on other maps.
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Conditional Score-Based Modeling of Effective Langevin Dynamics
A novel identity connects reduced-model drift and diffusion to the conditional score of the finite-time transition density, turning calibration into a least-squares problem over stationary lagged pairs that preserves invariant statistics and dynamical correlations.
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Reduced-Order Surrogates for Forced Flexible Mesh Coastal-Ocean Models
Koopman autoencoders with forcings and temporal unrolling deliver accurate year-long predictions for coastal-ocean models at 300-1400x speedup, outperforming POD in two of three cases.
-
Physiome-ODE: A Benchmark for Irregularly Sampled Multivariate Time Series Forecasting Based on Biological ODEs
Physiome-ODE is a new benchmark consisting of 50 IMTS datasets derived from biological ODEs that shows ODE-based forecasting models performing better and differentiating more meaningfully than on the existing four datasets.
-
Crossed-Product von Neumann Algebras for Incompressible Navier--Stokes Flows and Spectral Complexity Indicators
Constructs crossed-product von Neumann algebras M_u from incompressible flows to define commutator-based tracial complexity functionals linked to determinants and entropy.
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Tensor-based computation of the Koopman generator via operator logarithm
A tensor train method computes the Koopman generator via operator logarithm while preserving low-rank structure for scalable identification of high-dimensional nonlinear dynamics.
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Learning the Koopman Operator using Attention Free Transformers
Koopman autoencoders with attention-free latent memory and online change-point re-encoding reduce long-horizon error on Duffing, Repressilator, and IRMA benchmarks while keeping low latency.
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Quantum mechanics for classical transport equations
Classical probabilistic transport equations are reformulated as quantum systems whose wave function obeys Schrödinger evolution and whose observables include non-commuting operators for statistical quantities.
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Non-intrusive Learning of Physics-Informed Spatio-temporal Surrogate for Accelerating Design
A non-intrusive framework combines Koopman autoencoders with a spatio-temporal surrogate to learn and predict physics-constrained dynamics of systems like 2D flow around a cylinder for unseen conditions.
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The Birth of Quantum Mechanics and the Dirac Equation
The Dirac equation emerged from multiple simultaneous contributions in 1928, with Kramers' independent work and modern derivations from Ehrenfest relations and hydrodynamics now detailed.
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From Classical to Quantum-Mechanical Data Assimilation: A Comparison between DATO and QMDA
DATO and QMDA represent substantially different assimilation paradigms with distinct advantages and limitations in interpretability, robustness, and scalability.
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Nelson's Stochastic Mechanics: Measurement, Nonlocality, and the Classical Limit
Nelson's stochastic mechanics supplies a configuration-space diffusion picture where the Born rule is built-in, collapse is not an extra axiom, and nonlocality is softened, while proposing a distance scale to test limits of Bell correlations.
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Note About Koopman-von Neumann Theory and Density Matrix
The note argues that the classical N-particle distribution equals the diagonal of the density matrix operator in coordinate representation and derives a generalized BBGKY hierarchy for reduced density matrices.