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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Bayesian Physics Informed Spatio-Temporal Network for Streamflow Data Imputation

Reliable reconstruction of incomplete streamflow records is critical for improving hydrological forecasting, flood preparedness, and water resource management. However, large observational gaps and uncertainties in governing physical parameters limit the accuracy of traditional statistical and machinelearning imputation frameworks. To address these challenges, we develop a Bayesian Physics-Informed Spatio-Temporal Network (BPI-STNet) that jointly captures spatial and temporal dependencies while enforcing hydrologic consistency through embedded physical constraints. The framework integrates a GraphSAGE-LSTM architecture to model spatial connectivity across gauges and temporal flow dynamics, coupled with a Bayesian update mechanism to estimate uncertain parameters in a simplified water-balance framework. Unlike conventional physics-informed networks that rely on sampling-based posterior estimation, BPI-STNet derives an analytic solution to the inverse problem, allowing closed-form Bayesian updates of uncertain parameters Λ={α,β,k} using Gaussian priors and likelihoods. Applied to daily observations from the Susquehanna River Basin (1980-2022), BPI-STNet achieves substantial improvements over a purely data-driven RGNN baseline, which reduced RMSE by 23 % and MAE by 9 %, and achieving an average NSE values up to 0.96. The results demonstrate that coupling Bayesian inference with physics-informed learning yields physically consistent, uncertainty-aware reconstructions that preserve the temporal persistence and statistical distribution of observed flows. The proposed framework establishes a generalizable paradigm for data-sparse hydrologic systems where both data fidelity and physical interpretability are essential.

Krishnan Kutty Ambika, Anukesh [ORNL] (ORCID:00000↗
DOE OSTI2021

Integrated parameter and process learning for hydrologic and biogeochemical modules in Earth System Models

Focus area: Primary focal area #2; secondary focal area #3: Learning about parameters and processes of land surface hydrologic and biogeochemical models in Earth System models by integrating machine learning, physics, and big data. Science challenges: How do we maximally leverage big-data observations to improve hydrobiogeochemical process description and parameterization so that such modules more realistically capture hydrologic and vegetation responses and feedbacks under the future climate? For example, how can we leverage physics, limited observations of vegetation and streamflow to better estimate evapotranspiration, and, relatedly, net primary productivity, especially for drought areas? Vegetation plays a critical role in regional and global water cycles; however, existing vegetation models have failed to predict vegetation response to droughts (McDowell & Xu, 2017) , arctic greening (Keenan & Riley, 2018) , and critical transitions between forest and savanna (Hirota et al., 2011) . These studies suggest that when we build process-based models (PBM) parameterized from regional and global plant traits, we tend to poorly describe plant adaptation and local-scale competition processes. The models and their associated parameters assigned for different regions in the world are not capturing essential heterogeneity in vegetation responses at finer spatial scales. Many parameters of the land surface models control hydrology and vegetation dynamics at the same time. The heterogeneity in vegetation response is a function of (i) plant type, (ii) plant size, (iii) competition and succession, (iv) environmental controls, and (v) local variations due to the unique ecological community that are very difficult to describe (e.g., the size of gaps resulting from fire that facilitated the coexistence of pioneering species). In the demographic models, only factors (i) and (iv) were captured, and plant types were generally described only by leaf phenology and climate zones. With current demographic models, we generally consider more traits to define plant types (i) and calibrate these traits to consider factors (ii), (iii) and (iv); however, it is substantially challenging to scale to regional and global simulations due to trait variations across space (Ali et al., 2016). Moreover, it has been noted that hillslope processes, including ridge-to-valley flow and sunny vs. shady slopes are primary organizers of water, energy, and vegetation (Clark et al., 2015; Fan et al., 2019) . Although gradual improvements in the hydrologic model component in earth system models may reduce this error (at a remarkably slow pace), the long-term, gradual impact of hydrology on plant traits are not well captured. Recent work showed that the hydrologic controls exerted by groundwater and lateral flow are primary regulators of rooting depth (Fan et al., 2017) . Such hydrologic controls have seldom been reflected in vegetation model parameterizations.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1985

Computer architectures for computational physics work done by Computational Research and Technology Branch and Advanced Computational Concepts Group

Slides are reproduced that describe the importance of having high performance number crunching and graphics capability. They also indicate the types of research and development underway at Ames Research Center to ensure that, in the near term, Ames is a smart buyer and user, and in the long-term that Ames knows the best possible solutions for number crunching and graphics needs. The drivers for this research are real computational physics applications of interest to Ames and NASA. They are concerned with how to map the applications, and how to maximize the physics learned from the results of the calculations. The computer graphics activities are aimed at getting maximum information from the three-dimensional calculations by using the real time manipulation of three-dimensional data on the Silicon Graphics workstation. Work is underway on new algorithms that will permit the display of experimental results that are sparse and random, the same way that the dense and regular computed results are displayed.

Source record↗
NASA NTRS2005

Physics-Based Spectra of Accretion Disks around Black Holes

The purpose of this grant was to begin the process of deriving the light output of accretion disks around black holes directly from the actual processes that inject heat into the accreting matter, rather than from guessed dependences of heating rate on physical parameters. At JHU, the effort has focussed so far on models of accretion onto "intermediate mass black holes", a possible class of black holes, examples of which may have recently been discovered in nearby galaxies. There, Krolik and his student (Yawei Hui) have computed stellar atmospheres for uniformly-heated disks around this class of black holes. Their models serve two purposes: they are the very first serious attempts to compute the spectrum from accreting black holes in this mass range; and a library of such models can be used later in this program as contrasts for those computed on the basis of real disk dynamics. The output from these local disk calculations has also been successfully coupled to a program that applies the appropriate relativistic transformations and computes photon trajectories in order to predict the spectrum received by observers located at different polar angles. The principal new result of these calculations is the discovery of potentially observable ionization edges of H-like C and O at frequencies near the peak in flux from these objects. Most of the grant money at UCSB was spent on supporting graduate student Shane Davis. In addition. some money was spent on supporting two other students: Ari Socrates (now a Hubble Fellow at Princeton), and Laura Melling. Davis spent the year constructing stellar atmosphere models of accretion disks appropriate for the high/soft (thermal) state of black hole X-ray binaries. As with AGN models published previously by our collaboration with NASA support. our models include a complete general relativistic treatment of both the disk structure and the propagation of photons from the disk to a distant observer. They also include all important continuum opacity sources, including Compton scattering and bound-free opacity from abundant metal species. The principal new result is that bound-free opacity is very significant in altering the continuum spectral shape, resulting for example in quite different "color correction factors" compared to those predicted previously. In addition, the models predict a relationship between luminosity and inner disk temperature that is, for the first time, in accord with that observed. The primary purpose of the grant was to incorporate more realistic accretion disk physics, learned largely from simulations, into such spectral models. The Davis et al. paper includes consideration of a vertical dissipation profile computed from radiation magneto-hydrodynamic simulations of MRI turbulence by N. J. Turner (2004). So long as the disk is effectively thick, such dissipation profiles do not affect the predicted spectrum significantly. (More work needs to be done on these simulations, however.) A potentially more serious issue is that MRI turbulence produces substantial inhomogeneities, as do photon bubble instabilities. These inhomogeneities can affect the spectra by enhancing the effects of absorption opacity over scattering opacity. We have done some preliminary Monte Carlo calculations to explore these effects.

Krolik, Julian H.↗
NASA NTRS2018

Adventures in Low Disc Loading VTOL Design

This memoir covers the first eight years of my 37 year career in VTOL aircraft design. It starts with family and how I came to be an engineer with a passion for aviation and a desire to make a difference. At MIT I acquired a solid understanding of basic physics, learned the basics of the various engineering disciplines and gained design experience. After over a decade on the East Coast I was homesick for Northern California. I decided to take a chance on working for the government instead of industry in order to return home. I was hired by Dr. Richard M. Carlson in March 1975 and joined a wonderful Army/NASA technical environment. The Interservice Helicopter Commonality Study was an important introduction to Joint Service aircraft design. The Advanced Attack Helicopter Source Selection Evaluation Board was an opportunity to learn acquisition system fundamentals and to lead a small team in a major technical evaluation. The Advanced Scout Helicopter Concept Formulation was an opportunity to learn how an aircraft development program is created and it formed a partnership between Dr. Carlson's Labs and Charlie Crawford's Development and Qualification directorate. The Army was Executive Service for the first year (1982) of the Joint Services Advanced Vertical Lift Aircraft (JVX) program. The JVX Joint Technology Assessment concluded that there was at least one design configuration, the tilt rotor, which could satisfy all JVX mission requirements with a high degree of inter-service commonality. The Navy became Executive Service at the end of the year and promptly released a JVX RFP to industry. This RFP resulted in the V-22 Osprey tilt rotor as the third type of VTOL aircraft to enter production and service. I was very lucky to have a useful role early in this program.

VTOL Design↗
DOE OSTI2024

When ancient numerical demons meet physics-informed machine learning: adjoint-based gradients for implicit differentiable modeling

Recent advances in differentiable modeling, a genre of physics-informed machine learning that trains neural networks (NNs) together with process-based equations, have shown promise in enhancing hydrological models' accuracy, interpretability, and knowledge-discovery potential. Current differentiable models are efficient for NN-based parameter regionalization, but the simple explicit numerical schemes paired with sequential calculations (operator splitting) can incur numerical errors whose impacts on models' representation power and learned parameters are not clear. Implicit schemes, however, cannot rely on automatic differentiation to calculate gradients due to potential issues of gradient vanishing and memory demand. Here we propose a “discretize-then-optimize” adjoint method to enable differentiable implicit numerical schemes for the first time for large-scale hydrological modeling. The adjoint model demonstrates comprehensively improved performance, with Kling–Gupta efficiency coefficients, peak-flow and low-flow metrics, and evapotranspiration that moderately surpass the already-competitive explicit model. Therefore, the previous sequential-calculation approach had a detrimental impact on the model's ability to represent hydrological dynamics. Furthermore, with a structural update that describes capillary rise, the adjoint model can better describe baseflow in arid regions and also produce low flows that outperform even pure machine learning methods such as long short-term memory networks. The adjoint model rectified some parameter distortions but did not alter spatial parameter distributions, demonstrating the robustness of regionalized parameterization. Despite higher computational expenses and modest improvements, the adjoint model's success removes the barrier for complex implicit schemes to enrich differentiable modeling in hydrology.

58 GEOSCIENCES↗
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 OSTI2025

Physics-Informed Machine Learning Model for Ceramic Matrix Composite Creep

A physics-informed recurrent neural network (RNN) based surrogate model is developed to emulate the nonlinear, time-dependent constitutive behavior of ceramic matrix composites (CMCs) driven by matrix damage and constituent creep at the microscale. Physics-informed constraints are introduced into the surrogate model through regularization to ground the prediction in physics and improve its predictive capabilities. Training data is generated using the high-fidelity generalized method of cells (HFGMC) approach which calls appropriate creep and damage models for each of the constituents. This coupling permits simulating the nonlinear behavior of CMCs based on constituent response at the microscale along with microstructural features such as fiber and porosity volume fraction and fiber radius. The microscale repeating unit cell is loaded under creep fatigue conditions to replicate the material loading experienced in a turbine engine. Therefore, the RNN-based surrogate model is tasked with predicting, as a function of variable input stress sequence, temperature, and microstructural features, the resulting strain history response while satisfying physical constraints related to creep rate, isochoric inelastic deformation, and strain energy density. The trained surrogate model is shown to effectively match the strain history over quantified distributions of microstructural features and relevant loading regimes and temperatures. Neural network based surrogate models can offer efficient alternatives to running computationally intensive multiscale material models to simulate the nonlinear response of large structural models. Therefore, the presented work provides evidence towards the feasibility of developing, training, and running such models for CMCs with complex microstructures, nonlinear time-dependent material response, and under non-monotonic loading conditions.

ceramic matrix composites↗
DOE OSTI2021

Model fusion with physics-guided machine learning: Projection-based reduced-order modeling

The unprecedented amount of data generated from experiments, field observations, and large-scale numerical simulations at a wide range of spatiotemporal scales has enabled the rapid advancement of data-driven and especially deep learning models in the field of fluid mechanics. Although these methods are proven successful for many applications, there is a grand challenge of improving their generalizability. This is particularly essential when data-driven models are employed within outer-loop applications like optimization. In this work, we put forth a physics-guided machine learning (PGML) framework that leverages the interpretable physics-based model with a deep learning model. Leveraging a concatenated neural network design from multi-modal data sources, the PGML framework is capable of enhancing the generalizability of data-driven models and effectively protects against or inform about the inaccurate predictions resulting from extrapolation. We apply the PGML framework as a novel model fusion approach combining the physics-based Galerkin projection model and long- to short-term memory (LSTM) network for parametric model order reduction of fluid flows. We demonstrate the improved generalizability of the PGML framework against a purely data-driven approach through the injection of physics features into intermediate LSTM layers. Our quantitative analysis shows that the overall model uncertainty can be reduced through the PGML approach, especially for test data coming from a distribution different than the training data. Moreover, we demonstrate that our approach can be used as an inverse diagnostic tool providing a confidence score associated with models and observations. The proposed framework also allows for multi-fidelity computing by making use of low-fidelity models in the online deployment of quantified data-driven models.

42 ENGINEERING↗
DOE OSTI2024

Separable physics-informed DeepONet: Breaking the curse of dimensionality in physics-informed machine learning

The deep operator network (DeepONet) has shown remarkable potential in solving partial differential equations (PDEs) by mapping between infinite-dimensional function spaces using labeled datasets. However, in scenarios lacking labeled data, the physics-informed DeepONet (PI-DeepONet) approach, which utilizes the residual loss of the governing PDE to optimize the network parameters, faces significant computational challenges, particularly due to the curse of dimensionality. This limitation has hindered its application to high-dimensional problems, making even standard 3D spatial with 1D temporal problems computationally prohibitive. Additionally, the computational requirement increases exponentially with the discretization density of the domain. Here, to address these challenges and enhance scalability for high-dimensional PDEs, we introduce the Separable physics-informed DeepONet (Sep-PI-DeepONet). This framework employs a factorization technique, utilizing sub-networks for individual one-dimensional coordinates, thereby reducing the number of forward passes and the size of the Jacobian matrix required for gradient computations. By incorporating forward-mode automatic differentiation (AD), we further optimize computational efficiency, achieving linear scaling of computational cost with discretization density and dimensionality, making our approach highly suitable for high-dimensional PDEs. We demonstrate the effectiveness of Sep-PI-DeepONet through three benchmark PDE models: the viscous Burgers’ equation, Biot’s consolidation theory, and a parameterized heat equation. Our framework maintains accuracy comparable to the conventional PI-DeepONet while reducing training time by two orders of magnitude. Notably, for the heat equation solved as a 4D problem, the conventional PI-DeepONet was computationally infeasible (estimated 289.35 h), while the Sep-PI-DeepONet completed training in just 2.5 h. These results underscore the potential of Sep-PI-DeepONet in efficiently solving complex, high-dimensional PDEs, marking a significant advancement in physics-informed machine learning.

Neural operator↗
DOE OSTI2024

Anisotropic physics-regularized interpretable machine learning of microstructure evolution

Anisotropic Physics-Regularized Interpretable Machine Learning Microstructure Evolution (APRIMME) is a general-purpose machine learning solution for grain growth simulations. In prior work, PRIMME employed a deep neural network to predict site-specific migration as a function of its neighboring sites to model normal, isotropic, grain growth behavior. This work aims to extend this method by incorporating grain boundary misorientation-based grain growth behavior. APRIMME is trained on anisotropic simulations created using the Monte Carlo-Potts (MCP) model. Furthermore, the results of this work are compared statistically using grain radius, number of sides per grain, mean neighborhood misorientations, and the standard deviation of triple junction dihedral angles, and are found to match in most cases. The exceptions are small and seem to be related to two causes: (1) the deterministic model of APRIMME is learning from the stochastic simulations of MCP, which seems to accentuate triple junction behaviors; and, (2) a bias against very small grains is made evident in a quicker decrease in grains than expected at the beginning of an APRIMME simulation. APRIMME is also evaluated for its general ability to capture anisotropic grain growth behavior by first investigating different test case initial conditions, including a circle grain, three grain, and hexagonal grain microstructures.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Informing nuclear physics via machine learning methods with differential and integral experiments

Information from differential nuclear-physics experiments and theory is often too uncertain to accurately define nuclear-physics observables such as cross sections or energy spectra. Integral experimental data, representing the applications of these observables, are often more precise but depend simultaneously on too many of them to unambiguously identify issues in the observable with human expert analysis alone. Here, we explore how we can leverage physics knowledge gained from differential experimental data, nuclear theory, integral experiments, and neutron-transport calculations to better understand nuclear-physics observables in the context of the application area represented by integral experiments. We support this task with machine-learning methods to discern trends in a large amount of convoluted data. Differential and integral information was used in an analysis augmented by the random forest and the Shapley additive explanations metric. We chose as an application area one that is represented by criticality measurements and pulsed-sphere neutron-leakage spectra. We show one representative example ( 241 Pu fission observables) where the combination of differential and integral information allowed to resolve issues in data representing these observables. As a starting point, the machine learning (ML) algorithms highlighted several observables as leading potentially to bias in simulating integral experiments. Differential information, paired with sensitivity to integral quantities, allowed us then to pinpoint one specific observable ( 241 Pu fission cross section) as the main driver of bias. The comparison to integral experiments, on the other hand, allowed us to indicate a likely reliable experiment among several discrepant ones for this observables. In other cases (e.g., 239 Pu observables), we were not able to resolve the confounding introduced by integral experiments but instead highlighted the need for targeted new experiments and theory developments to better constrain the nuclear-physics space for the application area represented by integral experiments. We were able to combine information from differential experimental data, nuclear-physics theory, integral experiments, and neutron-transport simulations of the latter experiments with the help of the random forest algorithm and expert judgment. This combination of knowledge allows to improve our description of nuclear-physics observables as applied to a particular application area.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Development and assessment of a reactor system prognosis model with physics-guided machine learning

Autonomous control systems provide recommendations to help operators in decision-making during plant operations ranging from normal operation to accident management. An important step of autonomous control is prognosis. In nuclear engineering domain, prognosis is the process of predicting future conditions of a system or equipment based on present signs and symptoms of a fault. The prognosis model allows predicting future reactor states for possible candidate control strategies so that the outcomes can be evaluated to determine the best control strategy. The prognosis model requires representing direct relationships between the symptoms and the predictions. In nuclear engineering, computational simulations are approximate representations of the operation of the real system. However, prognosis with computational simulations requires high computation power and time due to possible large number of scenarios. Necessary computation resources can be reduced with machine learning (ML) approach for fast predictions by building a surrogate function using the simulation data. A critical issue is, ML models are ignorant of physical knowledge, and these models approximate statistical relationships between the system variables. This ignorance can produce results that are inconsistent with physical laws, even if an optimal result is achieved from a mathematical point of view. Physics-guided machine learning (PGML) is an approach to tackle this issue. Here, this work formulates and illustrates a framework to guide development and assessment of the ML-based prognosis model for autonomous control systems. The development of the prognosis model considers the training of a ML model which consists of optimizing many aspects of the ML approach. The assessment of the prognosis model considers training data limitations and uncertainties of the ML approach. Prognosis models with standalone ML and PGML are developed and assessed on the loss-of-flow scenario of Experimental Breeder Reactor II. The results indicate that PGML based prognosis model has the best performance compared to other prognosis models.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

Physics-Informed Deep Learning for Reconstruction of Spatial Missing Climate Information in the Antarctic

Understanding the influence of the Antarctic on the global climate is crucial for the prediction of global warming. However, due to very few observation sites, it is difficult to reconstruct the rational spatial pattern by filling in the missing values from the limited site observations. To tackle this challenge, regional spatial gap-filling methods, such as Kriging and inverse distance weighted (IDW), are regularly used in geoscience. Nevertheless, the reconstructing credibility of these methods is undesirable when the spatial structure has massive missing pieces. Inspired by image inpainting, we propose a novel deep learning method that demonstrates a good effect by embedding the physics-aware initialization of deep learning methods for rapid learning and capturing the spatial dependence for the high-fidelity imputation of missing areas. We create the benchmark dataset that artificially masks the Antarctic region with ratios of 30%, 50% and 70%. The reconstructing monthly mean surface temperature using the deep learning image inpainting method RFR (Recurrent Feature Reasoning) exhibits an average of 63% and 71% improvement of accuracy over Kriging and IDW under different missing rates. With regard to wind speed, there are still 36% and 50% improvements. In particular, the achieved improvement is even better for the larger missing ratio, such as under the 70% missing rate, where the accuracy of RFR is 68% and 74% higher than Kriging and IDW for temperature and also 38% and 46% higher for wind speed. In addition, the PI-RFR (Physics-Informed Recurrent Feature Reasoning) method we proposed is initialized using the spatial pattern data simulated by the numerical climate model instead of the unified average. Compared with RFR, PI-RFR has an average accuracy improvement of 10% for temperature and 9% for wind speed. When applied to reconstruct the spatial pattern based on the Antarctic site observations, where the missing rate is over 90%, the proposed method exhibits more spatial characteristics than Kriging and IDW.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

GRIDS-Net: Inverse shape design and identification of scatterers via geometric regularization and physics-embedded deep learning

This study presents a deep learning based methodology for both remote sensing and design of acoustic scatterers. The ability to determine the shape of a scatterer, either in the context of material design or sensing, plays a critical role in many practical engineering problems. This class of inverse problems is extremely challenging due to their high-dimensional, nonlinear, and ill-posed nature. To overcome these technical hurdles, we introduce a geometric regularization approach for deep neural networks (DNN) based on non-uniform rational B-splines (NURBS) and capable of predicting complex 2D scatterer geometries in a parsimonious dimensional representation. Then, this geometric regularization is combined with physics-embedded learning and integrated within a robust convolutional autoencoder (CAE) architecture to accurately predict the shape of 2D scatterers in the context of identification and inverse design problems. Further, an extensive numerical study is presented in order to showcase the remarkable ability of this approach to handle complex scatterer geometries while generating physically-consistent acoustic fields. The study also assesses and contrasts the role played by the (weakly) embedded physics in the convergence of the DNN predictions to a physically consistent inverse design.

42 ENGINEERING↗
DOE OSTI2026

Reactive Transport Modeling with Physics-Informed Machine Learning for Critical Minerals Applications

This study presents a physics-informed neural network (PINN) framework for reactive transport modeling for simulating fast bimolecular reactions in porous media. Accurate characterization of cAhemical interactions and product formation in surface and subsurface environments is essential for advancing critical mineral extraction and related geoscience applications. The proposed methodology sequentially addresses the flow and diffusion–reaction subproblems. The flow field is computed using a mixed formulation, while the diffusion–reaction system is modeled via two uncoupled tensorial diffusion equations reformulated in terms of chemical invariants. PINNs are employed to solve the governing equations, enabling data-efficient, mesh-free prediction of chemical concentration fields. The framework is validated through a series of benchmark problems involving flow in heterogeneous porous media. Initial verification is conducted using patch tests for the flow field, followed by validation of the transport problem with emphasis on preserving non-negativity of concentrations. The complete fast bimolecular reaction scenario is then solved, yielding spatial distributions of reactants and product species. Results demonstrate that the PINNs-based approach effectively captures sharp, mixing-limited reaction fronts and dispersive mixing behavior, offering reliable predictions of reactive plume evolution. These capabilities are crucial for evaluating long-term subsurface behavior in applications such as fluid storage, energy extraction, and efficient extraction of critical minerals.

42 ENGINEERING↗
DOE OSTI2022

Physics-Informed Machine Learning of Dynamical Systems for Efficient Bayesian Inference

Although the no-u-turn sampler (NUTS) is a widely adopted method for performing Bayesian inference, it requires numerous posterior gradients which can be expensive to compute in practice. Recently, there has been a significant interest in physics-based machine learning of dynamical (or Hamiltonian) systems and Hamiltonian neural networks (HNNs) is a noteworthy architecture. But these types of architectures have not been applied to solve Bayesian inference problems efficiently. We propose the use of HNNs for performing Bayesian inference efficiently without requiring numerous posterior gradients. We introduce latent variable outputs to HNNs (L-HNNs) for improved expressivity and reduced integration errors. We integrate L-HNNs in NUTS and further propose an online error monitoring scheme to prevent sampling degeneracy in regions where L-HNNs may have little training data. We demonstrate L-HNNs in NUTS with online error monitoring consider several complex high-dimensional posterior densities and compare its performance to NUTS.

97 MATHEMATICS AND COMPUTING↗