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Results for “model discovery”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Sparsifying priors for Bayesian uncertainty quantification in model discovery

We propose a probabilistic model discovery method for identifying ordinary differential equations governing the dynamics of observed multivariate data. Our method is based on the sparse identification of nonlinear dynamics (SINDy) framework, where models are expressed as sparse linear combinations of pre-specified candidate functions. Promoting parsimony through sparsity leads to interpretable models that generalize to unknown data. Instead of targeting point estimates of the SINDy coefficients, we estimate these coefficients via sparse Bayesian inference. The resulting method, uncertainty quantification SINDy (UQ-SINDy), quantifies not only the uncertainty in the values of the SINDy coefficients due to observation errors and limited data, but also the probability of inclusion of each candidate function in the linear combination. UQ-SINDy promotes robustness against observation noise and limited data, interpretability (in terms of model selection and inclusion probabilities) and generalization capacity for out-of-sample forecast. Sparse inference for UQ-SINDy employs Markov chain Monte Carlo, and we explore two sparsifying priors: the spike and slab prior, and the regularized horseshoe prior. UQ-SINDy is shown to discover accurate models in the presence of noise and with orders-of-magnitude less data than current model discovery methods, thus providing a transformative method for real-world applications which have limited data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

CDRL: Certification-Driven Reinforcement Learning for Neutrino Flavor Model Discovery

Many scientific discovery problems require searching combinatorial hypothesis spaces under complex domain constraints. Reinforcement learning (RL) offers a promising approach, but existing methods rely on scalar rewards that provide limited information about why candidate solutions fail, leading agents to repeatedly explore invalid regions. We introduce Certification-Driven Reinforcement Learning (CDRL), a framework that leverages structured feedback from symbolic reasoning tools. When a candidate violates domain constraints, these tools produce certificates identifying the actions responsible for failure. CDRL converts these certificates into reusable constraints that eliminate classes of invalid solutions and guide exploration toward valid regions. We evaluate CDRL on neutrino flavor model discovery in theoretical particle physics, where the hypothesis space exceeds $10^{26}$ possible models, and compare it with the state-of-the-art RL approach previously used for this task. Across three theory spaces, CDRL achieves up to 1.95$\times$ higher valid model rates and up to 6.33$\times$ higher neutrino model rates while evaluating up to 4$\times$ fewer candidates. We further extract 40 interpretable rules from search trajectories using a post-hoc decision-tree framework and show that reusing them as soft constraints yields gains of up to 2$\times$ in valid model rates and 3$\times$ in neutrino model discovery across all three theory spaces. These results suggest that CDRL uncovers reusable structure in combinatorial search spaces and provides a general framework for scientific model discovery.

Jha, Piyush [Georgia Tech., Atlanta; Georgia Tech]↗
NASA NTRS1978

C-band radar pulse Doppler error: Its discovery, modeling, and elimination

The discovery of a C Band radar pulse Doppler error is discussed and use of the GEOS 3 satellite's coherent transponder to isolate the error source is described. An analysis of the pulse Doppler tracking loop is presented and a mathematical model for the error was developed. Error correction techniques were developed and are described including implementation details.

Krabill, W. B.↗
DOE OSTI2024

Extreme sparsification of physics-augmented neural networks for interpretable model discovery in mechanics

Data-driven constitutive modeling with neural networks has received increased interest in recent years due to its ability to easily incorporate physical and mechanistic constraints and to overcome the challenging and time-consuming task of formulating phenomenological constitutive laws that can accurately capture the observed material response. However, even though neural network-based constitutive laws have been shown to generalize proficiently, the generated representations are not easily interpretable due to their high number of trainable parameters. Sparse regression approaches exist that allow for obtaining interpretable expressions, but the user is tasked with creating a library of model forms which by construction limits their expressiveness to the functional forms provided in the libraries. Here, in this work, we propose to train regularized physics-augmented neural network-based constitutive models utilizing a smoothed version of $L^0$-regularization. This aims to maintain the trustworthiness inherited by the physical constraints, but also enables interpretability which has not been possible thus far on any type of machine learning-based constitutive model where model forms were not assumed a priori but were actually discovered. During the training process, the network simultaneously fits the training data and penalizes the number of active parameters, while also ensuring constitutive constraints such as thermodynamic consistency. We show that the method can reliably obtain interpretable and trustworthy constitutive models for compressible and incompressible hyperelasticity, yield functions, and hardening models for elastoplasticity, using synthetic and experimental data. This work aims to set a new paradigm for interpretable machine learning models in the broad area of solid mechanics where low and limited data is available along with prior knowledge of physical constraints that the learned maps need to obey. This paradigm can potentially be extended to a broader spectrum of scientific exploration.

Data-driven constitutive models↗
DOE OSTI2024

Physics-Reinforced Machine Learning Algorithms for Multiscale Closure Model Discovery

The central objective of this project was to address the challenge of modeling and simulating complex multiscale turbulence phenomena by leveraging physics-guided machine learning (PGML) and hybrid modeling approaches. By integrating physics-based methods with data-driven models, the research focused on achieving robust and scalable solutions for geophysical turbulence, enhancing numerical weather prediction and climate research tools. The project resulted in significant advancements in computational modeling paradigms, predictive tools for reduced-order modeling, and innovative algorithms for fluid dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Data-driven causal model discovery and personalized prediction in Alzheimer's disease

Abstract With the explosive growth of biomarker data in Alzheimer’s disease (AD) clinical trials, numerous mathematical models have been developed to characterize disease-relevant biomarker trajectories over time. While some of these models are purely empiric, others are causal, built upon various hypotheses of AD pathophysiology, a complex and incompletely understood area of research. One of the most challenging problems in computational causal modeling is using a purely data-driven approach to derive the model’s parameters and the mathematical model itself, without any prior hypothesis bias. In this paper, we develop an innovative data-driven modeling approach to build and parameterize a causal model to characterize the trajectories of AD biomarkers. This approach integrates causal model learning, population parameterization, parameter sensitivity analysis, and personalized prediction. By applying this integrated approach to a large multicenter database of AD biomarkers, the Alzheimer’s Disease Neuroimaging Initiative, several causal models for different AD stages are revealed. In addition, personalized models for each subject are calibrated and provide accurate predictions of future cognitive status.

Zheng, Haoyang (ORCID:0000000168358242)↗
NASA NTRS2010

Automated Discovery and Modeling of Sequential Patterns Preceding Events of Interest

The integration of emerging data manipulation technologies has enabled a paradigm shift in practitioners' abilities to understand and anticipate events of interest in complex systems. Example events of interest include outbreaks of socio-political violence in nation-states. Rather than relying on human-centric modeling efforts that are limited by the availability of SMEs, automated data processing technologies has enabled the development of innovative automated complex system modeling and predictive analysis technologies. We introduce one such emerging modeling technology - the sequential pattern methodology. We have applied the sequential pattern methodology to automatically identify patterns of observed behavior that precede outbreaks of socio-political violence such as riots, rebellions and coups in nation-states. The sequential pattern methodology is a groundbreaking approach to automated complex system model discovery because it generates easily interpretable patterns based on direct observations of sampled factor data for a deeper understanding of societal behaviors that is tolerant of observation noise and missing data. The discovered patterns are simple to interpret and mimic human's identifications of observed trends in temporal data. Discovered patterns also provide an automated forecasting ability: we discuss an example of using discovered patterns coupled with a rich data environment to forecast various types of socio-political violence in nation-states.

Rohloff, Kurt↗
NASA NTRS2016

Discovery and Modelling of a Flattening of the Positive Cyclotron Line/luminosity Relation in GX 304-1 with RXTE

The Rossi X-ray Timing Explorer (RXTE) observed four outbursts of the accreting Xray binary transient source, GX 304−1 in 2010 and 2011. We present results of detailed 3-100 keV spectral analysis of 69 separate observations, and report a positive correlation between cyclotron line parameters, as well as other spectral parameters, with power-law flux. The cyclotron line energy, width and depth versus flux, and thus luminosity, correlations show a flattening of the relationships with increasing luminosity, which are well described by quasi-spherical or disc accretion that yield the surface magnetic field to be ∼5 × 1012 Gauss. Since HEXTE (High Energy X-ray Timing Experiment) cluster A was fixed aligned with the Proportional Counter Array field of view and cluster B was fixed viewing a background region 1. ◦ 5 off of the source direction during these observations near the end of the RXTE mission, the cluster A background was estimated from cluster B events using HEXTEBACKEST. This made possible the detection of the ∼55 keV cyclotron line and an accurate measurement of the continuum. Correlations of all spectral parameters with the primary 2-10 keV power-law flux reveal it to be the primary driver of the spectral shape. The accretion is found to be in the collisionless shock braking regime.

Rothschild, Richard E.↗
DOE OSTI2023

Generating Mixed Patterns of Residential Segregation: An Evolutionary Approach

The Schelling model of residential segregation has demonstrated that even the slightest preference for neighbors of the same race can be amplified into community-wide segregation. However, these models are unable to simulate mixed, coexisting patterns of segregation and integration, which have been seen to exist in cities. Using evolutionary model discovery we demonstrate how including social factors beyond racial bias when modeling relocation behavior enables the emergence of strongly mixed patterns. Our results indicate that the emergence of mixed patterns is better explained by multiple factors influencing the decision to relocate; the most important being the interaction of nonlinear, rapidly diminishing racial bias with a recent, historical tendency to move. Additionally, preference for less isolated neighborhoods or preference for neighborhoods with longer residing neighbors may produce weaker mixed patterns. Finally, this work highlights the importance of exploring the influence of multiple hypothesized factors of decision making, and their interactions, within agent rules, when studying emergent outcomes generated by agent-based models of complex social systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Gaussian processes meet NeuralODEs: a Bayesian framework for learning the dynamics of partially observed systems from scarce and noisy data

We present a machine learning framework (GP-NODE) for Bayesian model discovery from partial, noisy and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of differentiable programming to propagate gradient information through ordinary differential equation solvers and perform Bayesian inference with respect to unknown model parameters using Hamiltonian Monte Carlo sampling and Gaussian Process priors over the observed system states. This allows us to exploit temporal correlations in the observed data, and efficiently infer posterior distributions over plausible models with quantified uncertainty. The use of the Finnish Horseshoe as a sparsity-promoting prior for free model parameters also enables the discovery of parsimonious representations for the latent dynamics. A series of numerical studies is presented to demonstrate the effectiveness of the proposed GP-NODE method including predator–prey systems, systems biology and a 50-dimensional human motion dynamical system. This article is part of the theme issue ‘Data-driven prediction in dynamical systems’.

Science & Technology - Other Topics↗
DOE OSTI2023

Encoding nonlinear and unsteady aerodynamics of limit cycle oscillations using nonlinear sparse Bayesian learning

This article investigates the applicability of a recently proposed, nonlinear sparse Bayesian learning (NSBL) algorithm to identify and estimate the complex aerodynamics of limit cycle oscillations. NSBL provides a semi-analytical framework for determining the data-optimal sparse model nested within a (potentially) over-parameterized model. This is particularly relevant to nonlinear dynamical systems where modelling approaches involve the use of physics-based and data-driven components. In such cases, the data-driven components, where analytical descriptions of the physical processes are not readily available, are often prone to overfitting, meaning that the empirical aspects of these models will often involve the calibration of an unnecessarily large number of parameters. While an overparameterized model may fit the observed data well, such models may be inadequate for making predictions in regimes that are different from those wherein the data were recorded. In view of this, it is desirable to not only calibrate the model parameters, but also identify the optimal compromise between data fit and model complexity. In this article, we exhibit the optimal model discovery for an aeroelastic system wherein the structural dynamics are well-known and described by a differential equation model, coupled with a semi-empirical aerodynamic model for laminar separation flutter, resulting in low-amplitude limit cycle oscillations (LCO). To illustrate the performance of the algorithm, in this article, we use synthetic data and demonstrate the ability of the algorithm to correctly rediscover the optimal model and model parameters, given a known data-generating model. The synthetic data are generated from a forward simulation of a known differential equation model with parameters selected so as to mimic the dynamics observed in wind-tunnel experiments. Subsequently, we demonstrate the performance of the algorithm for model selection using noisy LCO data from wind tunnel experiments. As there is no ground truth available for the experimental data case, we provide a comparison between NSBL and Bayesian model selection to validate the results, and demonstrate the use of NSBL as an efficient alternative to traditional methods.

97 MATHEMATICS AND COMPUTING↗