arXiv subjects

Helmut H. Strey

Publications and source records attributed to Helmut H. Strey.

4 recordsLinked to original sources

arXiv2025

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↗

arXiv2024

Parameter estimation from an Ornstein-Uhlenbeck process with measurement noise

This article aims to investigate the impact of noise on parameter fitting for an Ornstein-Uhlenbeck process, focusing on the effects of multiplicative and thermal noise on the accuracy of signal separation. To address these issues, we propose algorithms and methods that can effectively distinguish between thermal and multiplicative noise and improve the precision of parameter estimation for optimal data analysis. Specifically, we explore the impact of both multiplicative and thermal noise on the obfuscation of the actual signal and propose methods to resolve them. First, we present an algorithm that can effectively separate thermal noise with comparable performance to Hamilton Monte Carlo (HMC) but with significantly improved speed. We then analyze multiplicative noise and demonstrate that HMC is insufficient for isolating thermal and multiplicative noise. However, we show that, with additional knowledge of the ratio between thermal and multiplicative noise, we can accurately distinguish between the two types of noise when provided with a sufficiently large sampling rate or an amplitude of multiplicative noise smaller than thermal noise. Thus, we demonstrate the mechanism underlying an otherwise counterintuitive phenomenon: when multiplicative noise dominates the noise spectrum, one can successfully estimate the parameters for such systems after adding additional white noise to shift the noise balance.

stat.ML↗

arXiv2020

Ground-truth resting-state signal provides data-driven estimation and correction for scanner distortion of fMRI time-series dynamics

The fMRI community has made great strides in decoupling neuronal activity from other physiologically induced T2* changes, using sensors that provide a ground-truth with respect to cardiac, respiratory, and head movement dynamics. However, blood oxygenation level-dependent (BOLD) time-series dynamics are confounded by scanner artifacts, in complex ways that can vary not only between scanners but even, for the same scanner, between sessions. The lack of equivalent ground truth has thus far stymied the development of reliable methods for identification and removal of scanner-induced noise. To address this problem, we first designed and built a phantom capable of providing dynamic signals equivalent to that of the resting-state brain. Using the dynamic phantom, we quantified voxel-wise noise by comparing the ground-truth time-series with its measured fMRI data. We derived the following data-quality metrics: Standardized Signal-to-Noise Ratio (ST-SNR) and Dynamic Fidelity that can be directly compared across scanners. Dynamic phantom data acquired from four scanners showed scanner-instability multiplicative noise contributions of about 6-18% of the total noise. We further measured strong non-linearity in the fMRI response for all scanners, ranging between 8-19% of total voxels. To correct scanner distortion of fMRI time-series dynamics at a single-subject level, we trained a convolutional neural network (CNN) on paired sets of measured vs. ground-truth data. Tests on dynamic phantom time-series showed a 4- to 7-fold increase in ST-SNR and about 40-70% increase in Dynamic Fidelity after denoising. Critically, we observed that the CNN temporal denoising pushes ST-SNR > 1. Denoising human-data with ground-truth-trained CNN showed markedly increased detection sensitivity of resting-state networks.

physics.med-ph↗

arXiv2019

On the Estimation of Parameters from Time Traces originating from an Ornstein-Uhlenbeck Process

In this article, we develop a Bayesian approach to estimate parameters from time traces that originate from an overdamped Brownian particle in a harmonic potential, or Ornstein-Uhlenbeck process (OU). We show that least-square fitting the autocorrelation function, which is often the standard way of analyzing such data, is significantly underestimating the confidence intervals of the fitted parameters. Here, we develop a rigorous maximum likelihood theory that properly captures the underlying statistics. From the analytic solution, we found that there exists an optimal measurement spacing ($Δt = 0.7968 τ$) that maximizes the statistical accuracy of the estimate for the decay-time $τ$ of the process for a fixed number of samples $N$, which plays a similar role than the Nyquist-Shannon theorem for the OU-process. In summary, our results have strong implications for parameter estimation for processes that result in a single exponential decay in the autocorrelation function. Our analysis can directly be applied to single-component dynamic light scattering experiments or optical trap calibration experiments.

cond-mat.soft↗