Proves O((α_n n)^{-1/2}) convergence of GNDE trajectories and adjoints to Graphon-NDE limits on sparse random graphs, with DTO/OTD consistency and experimental support for zero-shot transfer.
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On Neural Differential Equations
27 Pith papers cite this work, alongside 120 external citations. Polarity classification is still indexing.
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representative citing papers
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.
Differentiable implosion modeling enables gradient-based optimization of 500-parameter laser pulses for 25 kJ direct-drive ICF implosions on OMEGA-scale targets.
LIMINAL fits nested Lindblad models to tomographic data and uses likelihood-ratio tests to identify minimal dynamics for a five-qubit superconducting processor, supporting three-local Hamiltonian terms and two-local dissipation but not three-local dissipation.
Flow matching on time series targets a closed-form nonparametric velocity field that is a similarity-weighted mixture of observed transition velocities, making neural models approximations to an ideal memory-augmented dynamical system sampler.
AMIGO is an end-to-end differentiable forward model of JWST AMI that corrects detector systematics to recover high-precision astrometry and detect close high-contrast companions.
Extends scattered-wave-function and open-worldline-instanton methods to multidimensional curved spacetimes and demonstrates agreement on 2D metric examples.
A framework for online forecast reconciliation is developed via multivariate linear models on graph hierarchies, ridge regression, and recursive least squares, with a demonstration on district heating load data.
GaRA generates task-specific LoRA weight updates conditioned on graph structures to enable better whole-graph encoding in LLMs for zero-shot graph learning.
A Latent NCDE-based continuous-time probabilistic corrector wrapped around deterministic physics propagators like GMAT improves forecast accuracy and produces sharp calibrated full-covariance uncertainty estimates on real CDDIS data for 2-4 day horizons.
Stochastic Lifting adds random labels to training transitions to train a regression model that generates diverse stochastic trajectories without collapsing to mean predictions.
The Inverter framework formalizes inverse learning to generate coherent multi-step trajectories, outperforming offline RL and diffusion baselines on D4RL maze tasks by 24% on average with 10-100x less inference time while also matching GRAPE fidelity on single-qubit gates at >1000x speed.
NHODE framework learns partially observed dynamical systems by combining Hamiltonian neural networks with neural ODEs, enforcing energy conservation and improving long-horizon stability over data-driven baselines on mass-spring and three-body problems.
Derives RAM, a reward-adjusted consistency loss extending diffusion pretraining regression to efficient KL-regularized RL post-training, achieving peak rewards up to 50x faster than Flow-GRPO on Stable Diffusion 3.5M.
NSP model fuses satellite and gauge data with neural processes and SDEs, outperforming 13 baselines and JAXA's operational product on a new 43k-sample US benchmark across six metrics.
A pathwise Zakai-equation control formulation is used to train conditional neural SDEs that amortize nonlinear filtering of partially observed stochastic dynamics.
Neural CDEs serve as correctors that reduce error accumulation in multi-step forecasts from learned time-series models across synthetic, physics, and real-world data.
Global multiqubit Rydberg gates enable break-even measurement-free QEC and lower-shuttling Floquet codes in neutral-atom hardware.
Neptune infers spatiotemporal parameter fields in PDEs from as few as 45 sparse measurements using independent coordinate neural networks, outperforming PINNs and neural operators with lower errors and better extrapolation.
ShockCast is a two-phase ML method that predicts adaptive timestep sizes to model high-speed flows with shocks more efficiently than fixed-step approaches.
FNODE projects Neural ODE dynamics into the frequency domain via FFT and reports better generalization and convergence stability than GRUs, LSTMs, and ANODE on Lotka-Volterra, forced Duffing, Van der Pol, and Lorenz systems.
Introduces models for neural ODEs trained with online SGD and derives their high-dimensional learning curves via dynamical mean field theory.
Neural networks can detect 38% of summer hypoxic events shelf-wide from satellites with 47% precision, but only within the homogeneous mixed layer.
MPG-NODEs identify power system dynamics more flexibly than standard neural ODEs by using graph message passing, enabling transfer learning for adding or removing lines and units.
citing papers explorer
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Zero-Shot Size Transfer for Neural ODEs on Sparse Random Graphs: Graphon Limits and Adjoint Convergence
Proves O((α_n n)^{-1/2}) convergence of GNDE trajectories and adjoints to Graphon-NDE limits on sparse random graphs, with DTO/OTD consistency and experimental support for zero-shot transfer.
-
Accelerating Simulation and Optimisation of Cyclic Adsorption Processes with Differentiable Programming
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.
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High-dimensional inverse design of inertial fusion implosions via differentiable simulation
Differentiable implosion modeling enables gradient-based optimization of 500-parameter laser pulses for 25 kJ direct-drive ICF implosions on OMEGA-scale targets.
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Learning Lindblad Dynamics of a Superconducting Quantum Processor
LIMINAL fits nested Lindblad models to tomographic data and uses likelihood-ratio tests to identify minimal dynamics for a five-qubit superconducting processor, supporting three-local Hamiltonian terms and two-local dissipation but not three-local dissipation.
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Is Flow Matching Just Trajectory Replay for Sequential Data?
Flow matching on time series targets a closed-form nonparametric velocity field that is a similarity-weighted mixture of observed transition velocities, making neural models approximations to an ideal memory-augmented dynamical system sampler.
-
AMIGO: a Data-Driven Calibration of the JWST Interferometer
AMIGO is an end-to-end differentiable forward model of JWST AMI that corrects detector systematics to recover high-precision astrometry and detect close high-contrast companions.
-
Scattered wave functions and worldline instantons for particle production in curved spacetime
Extends scattered-wave-function and open-worldline-instanton methods to multidimensional curved spacetimes and demonstrates agreement on 2D metric examples.
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Online forecast reconciliation using linear models
A framework for online forecast reconciliation is developed via multivariate linear models on graph hierarchies, ridge regression, and recursive least squares, with a demonstration on district heating load data.
-
Enhancing LLMs for Graph Tasks via Graph-aware LoRA Generation
GaRA generates task-specific LoRA weight updates conditioned on graph structures to enable better whole-graph encoding in LLMs for zero-shot graph learning.
-
Continuous-Time Probabilistic Correctors for Uncertainty-Aware Physics-Based Spacecraft Trajectory Forecasting
A Latent NCDE-based continuous-time probabilistic corrector wrapped around deterministic physics propagators like GMAT improves forecast accuracy and produces sharp calibrated full-covariance uncertainty estimates on real CDDIS data for 2-4 day horizons.
-
Stochastic Lifting for Generating Trajectories of Stochastic Physical Systems
Stochastic Lifting adds random labels to training transitions to train a regression model that generates diverse stochastic trajectories without collapsing to mean predictions.
-
Neuro-Inspired Inverse Learning for Planning and Control
The Inverter framework formalizes inverse learning to generate coherent multi-step trajectories, outperforming offline RL and diffusion baselines on D4RL maze tasks by 24% on average with 10-100x less inference time while also matching GRAPE fidelity on single-qubit gates at >1000x speed.
-
Learning partially observed systems with neural Hamiltonian ordinary differential equations
NHODE framework learns partially observed dynamical systems by combining Hamiltonian neural networks with neural ODEs, enforcing energy conservation and improving long-horizon stability over data-driven baselines on mass-spring and three-body problems.
-
Reinforce Adjoint Matching: Scaling RL Post-Training of Diffusion and Flow-Matching Models
Derives RAM, a reward-adjusted consistency loss extending diffusion pretraining regression to efficient KL-regularized RL post-training, achieving peak rewards up to 50x faster than Flow-GRPO on Stable Diffusion 3.5M.
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Neural Stochastic Processes for Satellite Precipitation Refinement
NSP model fuses satellite and gauge data with neural processes and SDEs, outperforming 13 baselines and JAXA's operational product on a new 43k-sample US benchmark across six metrics.
-
Pathwise Learning of Stochastic Dynamical Systems with Partial Observations
A pathwise Zakai-equation control formulation is used to train conditional neural SDEs that amortize nonlinear filtering of partially observed stochastic dynamics.
-
Neural CDEs as Correctors for Learned Time Series Models
Neural CDEs serve as correctors that reduce error accumulation in multi-step forecasts from learned time-series models across synthetic, physics, and real-world data.
-
Multiqubit Rydberg Gates for Quantum Error Correction
Global multiqubit Rydberg gates enable break-even measurement-free QEC and lower-shuttling Floquet codes in neutral-atom hardware.
-
Estimating Parameter Fields in Multi-Physics PDEs from Scarce Measurements
Neptune infers spatiotemporal parameter fields in PDEs from as few as 45 sparse measurements using independent coordinate neural networks, outperforming PINNs and neural operators with lower errors and better extrapolation.
-
A Two-Phase Deep Learning Framework for Adaptive Time-Stepping in High-Speed Flow Modeling
ShockCast is a two-phase ML method that predicts adaptive timestep sizes to model high-speed flows with shocks more efficiently than fixed-step approaches.
-
Frequency-Domain Neural ODEs for Modeling Non-Linear Dynamical Systems
FNODE projects Neural ODE dynamics into the frequency domain via FFT and reports better generalization and convergence stability than GRUs, LSTMs, and ANODE on Lotka-Volterra, forced Duffing, Van der Pol, and Lorenz systems.
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Theory of learning of high-dimensional controlled non-linear dynamical systems (I): models and methods
Introduces models for neural ODEs trained with online SGD and derives their high-dimensional learning curves via dynamical mean field theory.
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The Physical Limit of Neural Hypoxia Detection in the Black Sea from Satellite Observations
Neural networks can detect 38% of summer hypoxic events shelf-wide from satellites with 47% precision, but only within the homogeneous mixed layer.
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Graph Neural Ordinary Differential Equations for Power System Identification
MPG-NODEs identify power system dynamics more flexibly than standard neural ODEs by using graph message passing, enabling transfer learning for adding or removing lines and units.
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A Weak Penalty Neural ODE for Learning Chaotic Dynamics from Noisy Time Series
Adding a weak-form penalty to the standard pointwise loss makes Neural ODE training robust to observation noise and preserves long-term invariant statistics on chaotic benchmarks and ERA5 climate data.
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Physics-constrained identification of graph-based thermal networks for spacecraft digital twins
A physics-constrained inverse-problem framework identifies graph-based lumped-parameter thermal models from temperature measurements for spacecraft digital-twin applications.
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Software Between Quantum and Machine Learning -- And Down to Pulses
Introduces a JAX-based framework for pulse-level QML with composable ansatze, end-to-end pulse optimization, and Fourier-analytic diagnostics.