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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Christopher Bishop.Pattern Recognition and Machine Learning
14 Pith papers cite this work. Polarity classification is still indexing.
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Cast3 translates NWP principles into a data-driven model using cubed-sphere grids, super-ensembles, and generative nudging to achieve state-of-the-art ensemble predictions that outperform baselines.
A new linearized dynamics based on the anti-symmetric part of the stability matrix preserves phase space volume for non-Hamiltonian chaotic systems within a classical density matrix framework.
Sparse hierarchies of K coupled gyrostats (M=2K+1 modes, no linear feedback) possess exactly (M+1)/2 quadratic invariants recoverable as Casimirs of a constructible non-canonical Poisson structure.
New dynamical series from Morse flow loops in fibered knot complements conjectured to equal BPS q-series encoding colored Jones polynomials, with proof for braid-homogeneous knots.
A framework recasts multivariate time series forecasting as scalar regression problems that tabular prior-fitted networks can solve zero-shot while addressing inter-channel interactions.
MASF redesigns the forward diffusion process to align with measurements, yielding a theoretically grounded likelihood score and up to 28.2x speedup on O(10^5)-dimensional Kolmogorov flow under sparse and nonlinear observation operators.
HealDA supplies ML-based initial conditions for AI weather models that produce forecasts trailing ERA5-initialized runs by less than one day of effective lead time, with the skill gap arising mainly from initial error size.
GIFT fine-tunes deep RL policies with a stability-focused reward to improve global stability while preserving task performance.
A quantum echo-state network is implemented on NISQ superconducting qubits and shown to predict long chaotic trajectories from the Lorenz system with memory persisting over 100 times the median T1/T2 time.
WSINDYc-MPC identifies governing dynamics more robustly than benchmarks under high noise, enabling longer prediction horizons and lower tracking errors in fusion, drone, chaos, and aircraft control tasks.
On the Lorenz model, 4DVAR tracks the true trajectory better than the Ensemble Kalman Filter for 20% initial errors but both fail for 40% errors with only three observations; performance improves when all variables are observed.
citing papers explorer
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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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Cast3: Translating numerical weather prediction principles into data-driven forecasting
Cast3 translates NWP principles into a data-driven model using cubed-sphere grids, super-ensembles, and generative nudging to achieve state-of-the-art ensemble predictions that outperform baselines.
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Phase space volume preserving dynamics for non-Hamiltonian systems
A new linearized dynamics based on the anti-symmetric part of the stability matrix preserves phase space volume for non-Hamiltonian chaotic systems within a classical density matrix framework.
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Quadratic invariants and Hamiltonian structure in coupled gyrostat low-order model hierarchies
Sparse hierarchies of K coupled gyrostats (M=2K+1 modes, no linear feedback) possess exactly (M+1)/2 quadratic invariants recoverable as Casimirs of a constructible non-canonical Poisson structure.
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Flow loops and quantum groups
New dynamical series from Morse flow loops in fibered knot complements conjectured to equal BPS q-series encoding colored Jones polynomials, with proof for braid-homogeneous knots.
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Zero-shot Multivariate Time Series Forecasting Using Tabular Prior Fitted Networks
A framework recasts multivariate time series forecasting as scalar regression problems that tabular prior-fitted networks can solve zero-shot while addressing inter-channel interactions.
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Rethinking Forward Processes for Score-Based Nonlinear Data Assimilation in High Dimensions
MASF redesigns the forward diffusion process to align with measurements, yielding a theoretically grounded likelihood score and up to 28.2x speedup on O(10^5)-dimensional Kolmogorov flow under sparse and nonlinear observation operators.
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HealDA: Highlighting the importance of initial errors in end-to-end AI weather forecasts
HealDA supplies ML-based initial conditions for AI weather models that produce forecasts trailing ERA5-initialized runs by less than one day of effective lead time, with the skill gap arising mainly from initial error size.
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GIFT: Global stabilisation via Intrinsic Fine Tuning
GIFT fine-tunes deep RL policies with a stability-focused reward to improve global stability while preserving task performance.
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Quantum Observers: A NISQ Hardware Demonstration of Chaotic State Prediction Using Quantum Echo-state Networks
A quantum echo-state network is implemented on NISQ superconducting qubits and shown to predict long chaotic trajectories from the Lorenz system with memory persisting over 100 times the median T1/T2 time.
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WSINDy for Model Predictive Control with Applications to Fusion, Drones, and Chaos
WSINDYc-MPC identifies governing dynamics more robustly than benchmarks under high noise, enabling longer prediction horizons and lower tracking errors in fusion, drone, chaos, and aircraft control tasks.
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Comparing an Ensemble Kalman Filter to a 4DVAR Data Assimilation System in Chaotic Dynamics
On the Lorenz model, 4DVAR tracks the true trajectory better than the Ensemble Kalman Filter for 20% initial errors but both fail for 40% errors with only three observations; performance improves when all variables are observed.
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