arXiv subjects

Christopher V. Rackauckas

Publications and source records attributed to Christopher V. Rackauckas.

3 recordsLinked to original sources

arXiv2026

Scientific Machine Learning of Chaotic Systems Learns Reduced-Order Equations for Neural Populations

Extracting interpretable mathematical models from complex dynamical systems is difficult, especially for chaotic dynamics observed with noisy experimental data. We present PEM-UDE, a method that combines prediction-error methodology with universal differential equations to discover governing equations from limited, noise-corrupted observations. Prediction-error feedback smooths the chaotic optimization problem; for noise-free data generated within the model class, it preserves the data-consistent zero-loss set, whereas noise and model misspecification introduce a gain-dependent stability-bias trade-off. Preservation of the zero-loss set is not a guarantee of unique structural identifiability. We test the method on two benchmark chaotic systems, the Rossler attractor and a real electrical circuit, and recover the correct functional forms even when one observed dimension contains noise of five times the signal magnitude. The method also accepts prior knowledge of the system as an initial functional form, which we use to learn neural circuit equations that account for sparse connectivity, a feature missing from conventional neural mass models. Applied to a population of Izhikevich neurons, PEM-UDE yields a multi-scale neural mass model that ties single-neuron parameters to macroscopic network dynamics and predicts a relationship between connection density, dominant oscillation frequency, and synchrony. We test these predictions against three intracranial recording datasets from rat and human cortices. For the neuroscience application, the learned equations are a reduced-order closure for a specified simulated Izhikevich network family; the experimental recordings provide an indirect consistency check of predicted frequency and synchrony trends, not a direct fit of the equations to recordings.

cs.LG↗

arXiv2026

Acceleration of horizontal numerical advection for atmospheric modeling through surrogate modeling with temporal coarse-graining

Machine-learned surrogate modeling of advection may accelerate geoscientific models, but existing approaches have either achieved limited speedup or have sacrificed spatial resolution compared to the model they are trained to emulate. We developed a machine-learned solver that speeds up advection simulations without sacrificing spatial resolution through the use of temporal coarse-graining, where the model is trained to take larger integration steps than dictated by the Courant-Friedrich-Lewy (CFL) condition. Our solver framework includes a convolutional neural network that takes concentrations and CFL numbers as inputs and outputs mass flux. Our solvers emulate 10-day ground-level horizontal advection simulations with r$^2$ values against the baseline ranging from 0.60--0.98 with temporal coarsening factors of 4 to 32 times the baseline integration time step. Speed increases and accuracy decreases with increased coarsening, with $r^2 = 0.24$ in accuracy lost for every factor of 10 gained in speed, reaching a maximum 92$\times$ speedup while maintaining $r^2 = 0.60$. We deliberately trained our solvers only on January ground-level wind data to examine their ability to generalize across seasons and vertical heights. The 4$\times$-coarsened learned solver successfully reproduces simulations over 72 vertical levels. The 8$\times$--16$\times$ solvers (but not 32$\times$) emulate most vertical levels. The learned solvers also generalize well across seasons, except for instabilities in June and October. With additional fine-tuning, these learned solvers could be appropriate for operational use where trading accuracy for speed could be advantageous, such as in screening tools, in ensemble simulations, or with data assimilation.

physics.ao-ph↗

arXiv2023

Signal Enhancement for Magnetic Navigation Challenge Problem

Harnessing the magnetic field of the Earth for navigation has shown promise as a viable alternative to other navigation systems. A magnetic navigation system collects its own magnetic field data using a magnetometer and uses magnetic anomaly maps to determine the current location. The greatest challenge with magnetic navigation arises when the magnetic field measurements from the magnetometer encompass the magnetic field from not just the Earth, but also from the vehicle on which it is mounted. It is difficult to separate the Earth magnetic anomaly field, which is crucial for navigation, from the total magnetic field reading from the sensor. The purpose of this challenge problem is to decouple the Earth and aircraft magnetic signals in order to derive a clean signal from which to perform magnetic navigation. Baseline testing on the dataset has shown that the Earth magnetic field can be extracted from the total magnetic field using machine learning (ML). The challenge is to remove the aircraft magnetic field from the total magnetic field using a trained model. This challenge offers an opportunity to construct an effective model for removing the aircraft magnetic field from the dataset by using a scientific machine learning (SciML) approach comprised of an ML algorithm integrated with the physics of magnetic navigation.

cs.LG↗