Using Conservation Laws to Infer Deep Learning Model Accuracy of Richtmyer-Meshkov Instabilities
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Mathematics and Computing↗
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Results for “Model Inference”
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Non-Intrusive Inference Reduced Order Model for Fluids Using Deep Multistep Neural Network
In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical engineering applications. Classical projection-based model reduction methods generate reduced systems by projecting full-order differential operators into low-dimensional subspaces. However, these techniques usually lead to severe instabilities in the presence of highly nonlinear dynamics, which dramatically deteriorates the accuracy of the reduced-order models. In contrast, our new framework exploits linear multistep networks, based on implicit Adams–Moulton schemes, to construct the reduced system. The advantage is that the method optimally approximates the full order model in the low-dimensional space with a given supervised learning task. Moreover, our approach is non-intrusive, such that it can be applied to other complex nonlinear dynamical systems with sophisticated legacy codes. We demonstrate the performance of our method through the numerical simulation of a two-dimensional flow past a circular cylinder with Reynolds number Re = 100. The results reveal that the new data-driven model is significantly more accurate than standard projection-based approaches.
97 MATHEMATICS AND COMPUTING↗
Inference of Crud Model Parameters from Plant Data
Over the past several years, the Virtual Environment forReactor Analysis, VERA, has provided a novel capability forthe Consortium for Advanced Simulation of Light Water Re-actors (CASL) to modelcrud-induced power shift (CIPS) inreactors operated by the Tennessee Valley Authority (TVA).While this developed capability in VERA is unique, multiplekey parameters in the crud physics have remained unknown.The methodology employed here provides the capability toinfer these key model parameters from measured plant data.Once the model parameters have been determined, a forwardVERA computation is performed and results are comparedto measured flux map data to determine the ecacy of thecalibrated crud model.
Collins, Benjamin↗
Enabling uncertainty quantification and propagation in combustion models using statistical inference of unreported experimental data.
Abstract not provided.
Najm, Habib N.↗
Multimodel ensemble predictions of precipitation using bayesian neural networks
Multimodel ensembling improves predictions and considers model uncertainties. In this study, we present a Bayesian Neural Network (BNN) ensemble approach for large-scale precipitation predictions based on a set of climate models. BNN infers spatiotemporally varying model weights and biases through the calibration against observations. This ensemble scheme of BNN sufficiently leverages individual model skill for accurate predictions as well as provides interpretability about which models contribute more to the ensemble prediction at which locations and times to inform model development. Additionally, BNN accurately quantifies epistemic uncertainty to avoid overconfident projections. We demonstrate BNN’s superior prediction performance to three state-of-the-art ensemble approaches and discuss its interpretability and uncertainty quantification.
Fan, Patrick↗
Multimodel Ensemble Predictions of Precipitation using Bayesian Neural Networks
Multimodel ensembling improves predictions and considers model uncertainties. In this study, we present a Bayesian Neural Network (BNN) ensemble approach for large-scale precipitation predictions based on a set of climate models. BNN infers spatiotemporally varying model weights and biases through the calibration against observations. This ensemble scheme of BNN sufficiently leverages individual model skill for accurate predictions as well as provides interpretability about which models contribute more to the ensemble prediction at which locations and times to inform model development. Additionally, BNN accurately quantifies epistemic uncertainty to avoid overconfident projections. We demonstrate BNN’s superior prediction performance to three state-of-the-art ensemble approaches and discuss its interpretability and uncertainty quantification.
Fan, Patrick↗
Exact and efficient hybrid Monte Carlo algorithm for accelerated Bayesian inference of gene expression models from snapshots of single-cell transcripts
Single cells exhibit a significant amount of variability in transcript levels, which arises from slow, stochastic transitions between gene expression states. Elucidating the nature of these states and understanding how transition rates are affected by different regulatory mechanisms require state-of-the-art methods to infer underlying models of gene expression from single cell data. A Bayesian approach to statistical inference is the most suitable method for model selection and uncertainty quantification of kinetic parameters using small data sets. However, this approach is impractical because current algorithms are too slow to handle typical models of gene expression. To solve this problem, we first show that time-dependent mRNA distributions of discrete-state models of gene expression are dynamic Poisson mixtures, whose mixing kernels are characterized by a piecewise deterministic Markov process. Here, we combined this analytical result with a kinetic Monte Carlo algorithm to create a hybrid numerical method that accelerates the calculation of time-dependent mRNA distributions by 1000-fold compared to current methods. We then integrated the hybrid algorithm into an existing Monte Carlo sampler to estimate the Bayesian posterior distribution of many different, competing models in a reasonable amount of time. We demonstrate that kinetic parameters can be reasonably constrained for modestly sampled data sets if the model is known a priori. If there are many competing models, Bayesian evidence can rigorously quantify the likelihood of a model relative to other models from the data. We demonstrate that Bayesian evidence selects the true model and outperforms approximate metrics typically used for model selection.
59 BASIC BIOLOGICAL SCIENCES↗
Block-Structured Operator Inference for Coupled Multiphysics Model Reduction
This work presents a block-structured formulation of Operator Inference as a way to learn structured reduced-order models for multiphysics systems. The approach specifies the governing equation structure for each physics component and the structure of the coupling terms. Once the multiphysics structure is specified, the reduced-order model is learned from snapshot data following the nonintrusive Operator Inference methodology. In addition to preserving physical system structure, which in turn permits preservation of system properties such as stability and second-order structure, the block-structured approach has the advantages of reducing the overall dimensionality of the learning problem and admitting tailored regularization for each physics component. The numerical advantages of the block-structured formulation over a monolithic Operator Inference formulation are demonstrated for aeroelastic analysis, which couples aerodynamic and structural models. For the benchmark test case of the AGARD 445.6 wing, block-structured Operator Inference provides an average 20% online prediction speedup over monolithic Operator Inference across subsonic and supersonic flow conditions in both the stable and fluttering parameter regimes while preserving the accuracy achieved with monolithic Operator Inference.
42 ENGINEERING↗
Bayesian learning with Gaussian processes for low-dimensional representations of time-dependent nonlinear systems
This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that poses the problem of learning low-dimensional model terms as a regression of state space data and corresponding time derivatives by minimizing the residual of reduced system equations. Standard operator inference models perform well with accurate training data that are dense in time, but producing stable and accurate models when the state data are noisy and/or sparse in time remains a challenge. Another challenge is the lack of uncertainty estimation for the predictions from the operator inference models. Our approach addresses these challenges by incorporating Gaussian process surrogates into the operator inference framework to (1) probabilistically describe uncertainties in the state predictions and (2) procure analytical time derivative estimates with quantified uncertainties. The formulation leads to a generalized least-squares regression and, ultimately, reduced-order models that are described probabilistically with a closed-form expression for the posterior distribution of the operators. The resulting probabilistic surrogate model propagates uncertainties from the observed state data to reduced-order predictions. Furthermore, we demonstrate the method is effective for constructing low-dimensional models of two nonlinear partial differential equations representing a compressible flow and a nonlinear diffusion–reaction process, as well as for estimating the parameters of a low-dimensional system of nonlinear ordinary differential equations representing compartmental models in epidemiology.
Data-driven model reduction↗
Lattice Spring Model & Simulation Based Parameter Inference
Presentation of mathematical content of SDRD project related to subsidence and shock physics
97 MATHEMATICS AND COMPUTING↗
Developing an Evolutionary Baseline Model for Humans: Jointly Inferring Purifying Selection with Population History
Building evolutionarily appropriate baseline models for natural populations is not only important for answering fundamental questions in population genetics—including quantifying the relative contributions of adaptive versus nonadaptive processes—but also essential for identifying candidate loci experiencing relatively rare and episodic forms of selection (e.g., positive or balancing selection). Here, a baseline model was developed for a human population of West African ancestry, the Yoruba, comprising processes constantly operating on the genome (i.e., purifying and background selection, population size changes, recombination rate heterogeneity, and gene conversion). Specifically, to perform joint inference of selective effects with demography, an approximate Bayesian approach was employed that utilizes the decay of background selection effects around functional elements, taking into account genomic architecture. This approach inferred a recent 6-fold population growth together with a distribution of fitness effects that is skewed towards effectively neutral mutations. Importantly, these results further suggest that, although strong and/or frequent recurrent positive selection is inconsistent with observed data, weak to moderate positive selection is consistent but unidentifiable if rare.
59 BASIC BIOLOGICAL SCIENCES↗
Simulation-Based Inference for Neutrino Interaction Model Tuning
This project demonstrates, for the first time, the application of simulation-based inference (SBI) techniques to tune neutrino–nucleus interaction models. Using a mock dataset based on the MicroBooNE tuning of the GENIE event generator, our approach employs a Neural Posterior Estimator (NPE) with Masked Autoregressive Flows (MAF) to infer the posterior distributions of key GENIE parameters directly from simulated histograms. The workflow provides a scalable and amortized framework for performing likelihood-free inference in high-dimensional parameter spaces, offering a pathway to more efficient and uncertainty-aware model tuning for next-generation neutrino experiments such as DUNE and SBND.
Tame-Narvaez, KarlaMaria [Fermi National Accelerat↗
Learning unknown physics of non-Newtonian fluids
Here, we use physics-informed neural networks (PINNs) to learn viscosity models of two non-Newtonian systems (polymer melts and suspensions of particles) using only velocity measurements. For synthetic velocity data generated with the power-law viscosity model, the PINN-inferred viscosity model agrees with the analytical model for shear rates with large absolute values but deviates for shear rates near zero where the analytical model has an unphysical singularity. Once the viscosity model is learned the PINN method can solve the momentum conservation equation using only the boundary conditions.
42 ENGINEERING↗
Radar-Based Bayesian Estimation of Ice Crystal Growth Parameters within a Microphysical Model
The potential for polarimetric Doppler radar measurements to improve predictions of ice microphysical processes within an idealized model–observational framework is examined. In an effort to more rigorously constrain ice growth processes (e.g., vapor deposition) with observations of natural clouds, a novel framework is developed to compare simulated and observed radar measurements, coupling a bulk adaptive-habit model of vapor growth to a polarimetric radar forward model. Bayesian inference on key microphysical model parameters is then used, via a Markov chain Monte Carlo sampler, to estimate the probability distribution of the model parameters. The statistical formalism of this method allows for robust estimates of the optimal parameter values, along with (non-Gaussian) estimates of their uncertainty. To demonstrate this framework, observations from Department of Energy radars in the Arctic during a case of pristine ice precipitation are used to constrain vapor deposition parameters in the adaptive habit model. The resulting parameter probability distributions provide physically plausible changes in ice particle density and aspect ratio during growth. A lack of direct constraint on the number concentration produces a range of possible mean particle sizes, with the mean size inversely correlated to number concentration. Consistency is found between the estimated inherent growth ratio and independent laboratory measurements, increasing confidence in the parameter PDFs and demonstrating the effectiveness of the radar measurements in constraining the parameters. Furthermore, the combined Doppler and polarimetric observations produce the highest-confidence estimates of the parameter PDFs, with the Doppler measurements providing a stronger constraint for this case.
54 ENVIRONMENTAL SCIENCES↗
Improved time-delay lens modelling and H 0 inference with transient sources
ABSTRACT Strongly lensed explosive transients such as supernovae, gamma-ray bursts, fast radio bursts, and gravitational waves are very promising tools to determine the Hubble constant (H0) in the near future in addition to strongly lensed quasars. In this work, we show that the transient nature of the point source provides an advantage over quasars: The lensed host galaxy can be observed before or after the transient’s appearance. Therefore, the lens model can be derived from images free of contamination from bright point sources. We quantify this advantage by comparing the precision of a lens model obtained from the same lenses with and without point sources. Based on Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) observations with the same sets of lensing parameters, we simulate realistic mock data sets of 48 quasar lensing systems (i.e. adding AGN in the galaxy centre) and 48 galaxy–galaxy lensing systems (assuming the transient source is not visible but the time delay and image positions have been or will be measured). We then model the images and compare the inferences of the lens model parameters and H0. We find that the precision of the lens models (in terms of the deflector mass slope) is better by a factor of 4.1 for the sample without lensed point sources, resulting in an increase of H0 precision by a factor of 2.9. The opportunity to observe the lens systems without the transient point sources provides an additional advantage for time-delay cosmography over lensed quasars. It facilitates the determination of higher signal-to-noise stellar kinematics of the main deflector, and thus its mass density profile, which, in turn plays a key role in breaking the mass-sheet degeneracy and constraining H0.
Ding, Xuheng↗
Bayesian inference of heterogeneous epidemic models: Application to COVID-19 spread accounting for long-term care facilities
Here we propose a high dimensional Bayesian inference framework for learning heterogeneous dynamics of a COVID-19 model, with a specific application to the dynamics and severity of COVID-19 inside and outside long-term care (LTC) facilities. We develop a heterogeneous compartmental model that accounts for the heterogeneity of the time-varying spread and severity of COVID-19 inside and outside LTC facilities, which is characterized by time-dependent stochastic processes and time-independent parameters in ~ 1500 dimensions after discretization. To infer these parameters, we use reported data on the number of confirmed, hospitalized, and deceased cases with suitable post-processing in both a deterministic inversion approach with appropriate regularization as a first step, followed by Bayesian inversion with proper prior distributions. To address the curse of dimensionality and the ill-posedness of the high-dimensional inference problem, we propose use of a dimension-independent projected Stein variational gradient descent method, and demonstrate the intrinsic low-dimensionality of the inverse problem. We present inference results with quantified uncertainties for both New Jersey and Texas, which experienced different epidemic phases and patterns. Moreover, we also present forecasting and validation results based on the empirical posterior samples of our inference for the future trajectory of COVID-19.
42 ENGINEERING↗
Operator inference with roll outs for learning reduced models from scarce and low-quality data
Data-driven modeling has become a key building block in computational science and engineering. However, data that are available in science and engineering are typically scarce, often polluted with noise and affected by measurement errors and other perturbations, which makes learning the dynamics of systems challenging. Here, in this work, we propose to combine data-driven modeling via operator inference with the dynamic training via roll outs of neural ordinary differential equations. Operator inference with roll outs inherits interpretability, scalability, and structure preservation of traditional operator inference while leveraging the dynamic training via roll outs over multiple time steps to increase stability and robustness for learning from low-quality and noisy data. Numerical experiments with data describing shallow water waves and surface quasi-geostrophic dynamics demonstrate that operator inference with roll outs provides predictive models from training trajectories even if data are sampled sparsely in time and polluted with noise of up to 10%.
97 MATHEMATICS AND COMPUTING↗