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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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

MODELING AND OPTIMIZATION STUDY OF A TIGHTLY INTEGRATED ROTARY ELECTRIC MOTOR-HYDRAULIC PUMP

To meet the growing trend of electrification of mechanical systems, this paper presents a compactly integrated electric motor and hydraulic pump. The proposed application for this machine requires high flow rates at low pressure differentials and four quadrant operation. The hydraulic pump architecture selected for this machine is a radial ball piston pump. An inside impinged version of this architecture allows for efficient filling of the chambers and is radial balanced, both of which allow high- speed operation for increased power density. The radial ball piston pump is less expensive to manufacture and is radially more compact than a standard radial cylindrical piston pump. A model of the pump and the integrated electric motor have been created to study scaling relationships and drive detailed design and optimization. The scaling study considers how displacement is affected by pump diameter, and how the diameter and required torque change with angular velocity. The detailed model considers the effect of valve timing, piston-cylinder clearance, and pump geometry on the efficiency. The model is then exercised in an optimization of the machine parameters.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2024

Demonstration and Verification of Thermo-Mechanical Bowing in a Limited Free-Bow SFR Concept Using MOOSE

Core bowing due to thermal gradients and irradiation induced swelling and creep introduces significant reactivity feedback effects in liquid metal-cooled fast spectrum reactors. During startup, normal operations, and transient events, differential thermal and flux gradients cause expansion, creep, and swelling, which results in bowing in preferential directions depending on local material properties and load-pad and restraint-ring design. The bowing phenomenon produces negative reactivity during accident conditions provided the restraint system has been properly designed to optimally guide the deformation outwards in the active core region. Under the Department of Energy Nuclear Energy Advanced Modeling and Simulation program, a Multiphysics Object Oriented Simulation Environment (MOOSE)-based multiphysics approach to model core bowing is being developed. The present work expands on previous modeling of simpler International Atomic Energy Agency (IAEA) verification problems with these tools by modeling IAEA Verification Problem 4, which involves a symmetric sector of a reactor core with ducted assemblies undergoing differential thermal expansion due to thermal gradients bowing outward with duct-to-duct contact. This model is available on the National Reactor Innovation Center Virtual Test Bed repository. This example was verified against benchmark participant results, which includes bowing deformation evaluation and duct-to-duct interactions at load pads with mechanical contact.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2019

Gasification Combined Heat and Power from Coal Fines

The goal of this final project report is to comprehensively summarize the work for public domain conducted on project DE-FE 0031520. In accordance with the Statement of Project Objectives (SOPO), the University of Kentucky Center for Applied Energy Research (UKy-CAER) (Recipient) has completed a Front End Engineering Design (FEED) study 5 MWe polygeneration unit using the Coal Fields Regional Industrial Park in Hazard, Kentucky (KY) as a model location and using coal recovered from the adjacent Pads Branch Impoundment as feed. The scope of work is a thorough study that can be used as a template for the application of the proposed technology throughout Eastern KY and other coal communities nationwide. The Technology Design Basis was developed based on three elements: basic site characteristics; fuel feedstock; and environmental health and safety requirements. The Basic Engineering Design Elements include the preliminary process design (the process area descriptions; the Block Flow Diagram (BFD), Process Flow Diagrams (PFDs) and Piping and Instrumentation Diagrams (P&IDs), process simulation outputs and Heat and Mass Balance (H&MB) stream tables, the major process equipment and instrumentation lists which includes specifications and materials of construction); the cost estimate (capital cost estimate, operational cost estimate, and comparison with state-of-the-art commercial scale similar technologies, options to lower cost, construction cost and schedule estimate); and other supporting elements (guidelines for execution and management of the project), logistical summary, and balance of plant summary, the Environmental Health and Safety (EH&S) assessment; and a Social and Economic Impact (S&EI) assessment. All project milestones, deliverables and success criteria were met. The proposed 5 MWe polygeneration facility being fed from impoundment recovered coal has been shown to be technically feasible. Annual revenues are estimated at $\$ $2.4M from electricity, steam and hydrocarbon production; annual operating expenses are $\$ $5.2M ($\$ $2.9 M in operating expenses, and $\$ $2.4M in indirect expenses). The gasifier facility, as configured during the FEED, will lose money when operating under commercial operating conditions and terms. However, eight options improving the economics can be considered during the detailed design phase to make the facility profitable by taking advantage of the positive differential of revenue to variable operating costs, and reducing the influence of fixed operating costs. Coupled with the findings from the S&EI assessment estimating a total economic impact of $\$ $374M for the proposed polygeneration facility at >$\$ $1.5B, if three additional such projects are implemented, clearly positive economics are demonstrated. No EH&S issues are identified that would prohibit proceeding with the project, although permitting efforts are estimated to take 3-5 years.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2025

Optimal Control of Differentially Private EV Charging: A Scalable Learning Approach Under Uncertainty

Internet of Things (IoT)-enabled electric vehicles (IoEVs) enable intelligent charging coordination that accounts for grid congestion. However, increased data exchange raises privacy concerns, as charging patterns can reveal sensitive driver behavior to grid operators. Here, we propose a differentially private (DP) EV charging framework that enables coordinated control while protecting driver data with theoretical privacy guarantees. Nevertheless, integrating DP inevitably introduces uncertainty into the control strategy for EVs, which can lead to infeasible solutions. To tackle this challenge, we develop a feasible and scalable control algorithm based on constrained reinforcement learning (CRL) and convex hulls. While our framework is designed to handle the uncertainty introduced by DP, it is general and also applicable to other sources of uncertainty in EV charging, such as the stochastic nature of driver behavior and renewable variability. This ensures feasible and privacy-preserving coordination of EV charging at scale. Our method constructs convex hulls within the action space to guarantee feasibility under stochastic constraints and incorporates constraint reduction techniques to improve scalability. Case studies based on IEEE benchmark systems demonstrate that the proposed approach effectively balances feasibility under uncertainty, scalability, and privacy in large-scale EV charging control.

Engineering - Power transmission and distribution↗
DOE OSTI2023

Snekmer: a scalable pipeline for protein sequence fingerprinting based on amino acid recoding

Abstract Motivation The vast expansion of sequence data generated from single organisms and microbiomes has precipitated the need for faster and more sensitive methods to assess evolutionary and functional relationships between proteins. Representing proteins as sets of short peptide sequences (kmers) has been used for rapid, accurate classification of proteins into functional categories; however, this approach employs an exact-match methodology and thus may be limited in terms of sensitivity and coverage. We have previously used similarity groupings, based on the chemical properties of amino acids, to form reduced character sets and recode proteins. This amino acid recoding (AAR) approach simplifies the construction of protein representations in the form of kmer vectors, which can link sequences with distant sequence similarity and provide accurate classification of problematic protein families. Results Here, we describe Snekmer, a software tool for recoding proteins into AAR kmer vectors and performing either (i) construction of supervised classification models trained on input protein families or (ii) clustering for de novo determination of protein families. We provide examples of the operation of the tool against a set of nitrogen cycling families originally collected using both standard hidden Markov models and a larger set of proteins from Uniprot and demonstrate that our method accurately differentiates these sequences in both operation modes. Availability and implementation Snekmer is written in Python using Snakemake. Code and data used in this article, along with tutorial notebooks, are available at http://github.com/PNNL-CompBio/Snekmer under an open-source BSD-3 license. Supplementary information Supplementary data are available at Bioinformatics Advances online.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

On the effectiveness of neural operators at zero-shot weather downscaling

Machine-learning (ML) methods have shown great potential for weather downscaling. These data-driven approaches provide a more efficient alternative for producing high-resolution weather datasets and forecasts compared to physics-based numerical simulations. Neural operators, which learn solution operators for a family of partial differential equations, have shown great success in scientific ML applications involving physics-driven datasets. Neural operators are grid-resolution-invariant and are often evaluated on higher grid resolutions than they are trained on, i.e., zero-shot super-resolution. Given their promising zero-shot super-resolution performance on dynamical systems emulation, we present a critical investigation of their zero-shot weather downscaling capabilities, which is when models are tasked with producing high-resolution outputs using higher upsampling factors than are seen during training. To this end, we create two realistic downscaling experiments with challenging upsampling factors (e.g., 8x and 15x) across data from different simulations: the European Centre for Medium-Range Weather Forecasts Reanalysis version 5 (ERA5) and the Wind Integration National Dataset Toolkit. While neural operator-based downscaling models perform better than interpolation and a simple convolutional baseline, we show the surprising performance of an approach that combines a powerful transformer-based model with parameter-free interpolation at zero-shot weather downscaling. We find that this Swin-Transformer-based approach mostly outperforms models with neural operator layers in terms of average error metrics, whereas an Enhanced Super-Resolution Generative Adversarial Network-based approach is better than most models in terms of capturing the physics of the ground truth data. We suggest their use in future work as strong baselines.

17 WIND ENERGY↗
DOE OSTI2026

Evaluating Protection System Performance for a Real-World Weak Grid Area With High Inverter-Based Resources

This paper evaluates an existing protection scheme implemented in a real-world weak grid area with a high penetration of inverter-based resources (IBRs). The study aims to assess the reliability and adequacy of protection schemes originally designed for traditional synchronous machine systems and determine whether they can continue to operate reliably in systems with high levels of IBRs. Hardware relays are tested using a controller-hardware-in-the-loop setup. PSCAD electromagnetic transient simulation with an IBR original equipment manufacturer black-box model is used to perform fault studies and generate COMTRADE data, which are replayed by a realtime digital simulator (RTDS) to feed input to the hardware relays. Three scenarios are analyzed: normal operation, an N-1 contingency, and an IBR-only scenario. The evaluation results reveal the following: 1) the protection scheme remains reliable under normal conditions and N-1 contingencies and 2) in IBRonly scenarios, differential protection (87L) continues to operate reliably, whereas local protection elements, such as distance and directional elements, fail because of the lack of regulated negative sequence current contributed by IBRs. These findings provide utilities with valuable insights for improving their protection systems in high-IBRs.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

VALVE TIMING AND AREA PROFILE SELECTION FOR HYDRAULIC PUMPS AND MOTORS

A significant amount of research has been conducted to select valve timing and area profiles that create efficient and quiet hydraulic pumps and motors. Numerous active valve architectures have been modeled and optimized, but the rationale for the final solution is often unclear. The solution is usually highly dependent on the modeled valve geometry constraints and the duty cycle of the pump or motor for which the valve was optimized. This paper first presents an ideal valve area profile and what compromises are made to design for a working pressure and speed range. The ideal valve area profile is resolved using a piston-cylinder model with a pressure dependent bulk modulus and variable valve openings. The piston-cylinder is first modeled as a pump with passive (check) valves and a specified pressure drop across the valves to determine the ideal area profile. A generalization of the ideal timing is demonstrated for positive pressure differential and positive rotation direction, also known as the first quadrant. The effects on valve timing when varying pressure are shown for the first quadrant, but the trends can be extrapolated for all quadrants of operation. The ideal valve profile is implemented as fixed valve timing, meaning the valve area is only a function of the timing angle, in a pump-motor. The pump-motor is simulated in one rotation direction through a pressure range. Performance is high in pumping operation, but when the pressure differential is reversed, cylinder pressure spikes ensue. Two strategies to modify an ideal valve area profile are presented: timing grooves and a pressure shifted valve timing. Timing grooves reduce pressure spikes and cavitation in the cylinder but generally increase throttling losses. A pressure shifted valve timing has lower throttling energy losses, making it the favored solution.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Study of the Protection Improvements for a Weak Grid Area With High Inverter-Based Resources (IBRs)

This project designs enhanced protection scheme for the real-world weak grid area with a high penetration of IBRs. As the existing protection schemes are originally designed for traditional synchronous machines, we first evaluate if the protection scheme will continue to operate reliably in systems with high levels of IBRs. Hardware relays are tested using a controller-hardware-in-the-loop setup. PSCAD electromagnetic transient simulation with IBR original equipment manufacturer black-box models is used to perform fault studies and generate COMTRADE data, which are replayed by a real-time digital simulator (RTDS) to feed input to the hardware relays. Three scenarios are analyzed: normal operation, an N-1 contingency, and an IBR-only scenario. The evaluation results reveal the following: 1) the protection scheme remains reliable under normal conditions and N-1 contingencies and 2) in IBR-only scenarios, differential protection (87L) continues to operate reliably, whereas local protection elements, such as distance and directional elements, fail because of the lack of regulated negative sequence current contributed by IBRs. Enhanced protection is designed to address the challenge of lack of negative sequence current from IBRs, including increased restraining factors a2 and k2 to block 32Q or using V instead QV ORDER for ground faults, enhanced mho distance element with voltage and phase angle supervision for L-L faults. The efficacy of enhanced protection logic is validated and proven to work reliably. Additionally, IEEE Std. 2800-2022 negative sequence current compliant GFL and GFM IBRs from another vendor are tested and proven to work reliably without need for enhanced logic. Therefore, this work provides valuable decision-making for utilities facing protection system challenges due to IBRs, either designing enhanced protection scheme or requesting their IBRs being IEEE Std. 2800-2022 compliant to produce regulated negative sequence current for protection relay to make correct decision.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Evaluating Protection System Performance for a Real-World Weak Grid Area With High Inverter-Based Resources: Preprint

This paper evaluates an existing protection scheme implemented in a real-world weak grid area with a high penetration of inverter-based resources (IBRs). The study aims to assess the reliability and adequacy of protection schemes originally designed for traditional synchronous machine systems and determine whether they can continue to operate reliably in systems with high levels of IBRs. Hardware relays are tested using a controller-hardware-in-the-loop setup. PSCAD electromagnetic transient simulation with an IBR original equipment manufacturer black-box model is used to perform fault studies and generate COMTRADE data, which are replayed by a real-time digital simulator (RTDS) to feed input to the hardware relays. Three scenarios are analyzed: normal operation, an N-1 contingency, and an IBR-only scenario. The evaluation results reveal the following: 1) the protection scheme remains reliable under normal conditions and N-1 contingencies and 2) in IBR-only scenarios, differential protection (87L) continues to operate reliably, whereas local protection elements, such as distance and directional elements, fail because of the lack of regulated negative sequence current contributed by IBRs. These findings provide utilities with valuable insights for improving their protection systems in high-IBRs.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Applications of physics informed neural operators

Abstract We present a critical analysis of physics-informed neural operators (PINOs) to solve partial differential equations (PDEs) that are ubiquitous in the study and modeling of physics phenomena using carefully curated datasets. Further, we provide a benchmarking suite which can be used to evaluate PINOs in solving such problems. We first demonstrate that our methods reproduce the accuracy and performance of other neural operators published elsewhere in the literature to learn the 1D wave equation and the 1D Burgers equation. Thereafter, we apply our PINOs to learn new types of equations, including the 2D Burgers equation in the scalar, inviscid and vector types. Finally, we show that our approach is also applicable to learn the physics of the 2D linear and nonlinear shallow water equations, which involve three coupled PDEs. We release our artificial intelligence surrogates and scientific software to produce initial data and boundary conditions to study a broad range of physically motivated scenarios. We provide the source code , an interactive website to visualize the predictions of our PINOs, and a tutorial for their use at the Data and Learning Hub for Science .

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Evaluation of a Surface Spill Operation to Return Adult Steelhead Overshoots Downstream of McNary Dam

This study, funded by the U.S. Army Corps of Engineers (USACE), was conducted by the Pacific Northwest National Laboratory to evaluate the efficacy of operating one Top Spill Weir (TSW) at McNary Dam outside the normal TSW operation dates for juvenile salmon passage. Of interest is whether the TSW is an effective downstream passage route for adult steelhead overshoots. Overshoots are fish which, having passed upstream at McNary Dam, must pass downstream to return to their natal stream to spawn. This report covers Fall (2019) and Spring (2020) study periods. The study design arranged the available 24 hours of TSW spill per week into weekly blocks with sub-blocks differentiated into day and night operations with TSW discharge periods of 4- and 8-hours duration. Hydroacoustic techniques were used to sample adult fish passage at the TSW and at turbine units 1 and 10. The experimental design contrasted TSW spill periods of differing duration and at different times of the day. The small number of fish detected passing the TSW, and the smaller number of fish detected passing the turbine units, were best suited to an ad hoc, exploratory approach to evaluating the effect of TSW spill. It is worthwhile to note that the operations data obtained for the fall study period had a greater than expected number of gaps and apparent anomalies that we believe were a result of how the data were aggregated. These problems are not particularly problematic for the present study, because the available data still provide a good indication of whether the TSW was operating at each point in time. TSW flows in both fall and spring data sets were able to be cleaned up using the established relationship between forebay elevation and TSW discharge rate. Additional cleanup of operations data would be needed, however, if more quantitative evaluation of dam-wide flow and passage relationships were needed. This study contrasted TSW spill periods of differing duration and at different times of the day. The small number of fish detected passing the TSW, and the smaller number of fish detected passing the turbine units were best suited to an ad hoc, exploratory approach to evaluating the effect of TSW spill. Spring adult steelhead passage numbers estimated using hydroacoustics were notably lower than during the fall study period, and that was consistent with our analysis of PIT tagged fish likely to be in the vicinity during each study period. Detections of fish in BlueView sampling areas upstream of the TSW and powerhouse were not correlated with detections of fish passing hydroacoustic sampling areas, which suggests that fish approaching the face of the dam can move around the forebay before passing. Other fish detected in the forebay in large numbers, such as shad, were able to be filtered out of steelhead passage counts and did not appear to be influencing hydroacoustic passage rate estimates. A pulse of passage at the initial TSW opening was weakly evident, but trends across 4- and 8-hour operational periods did not show a distinct decline in passage over time as TSW operation continued. Our findings do not indicate a reason to choose one 8-hour period over two 4-hour periods, or vice versa. This suggests that the duration of spill periods can be chosen based on operational or other considerations. Passage rates were consistently higher during the daytime TSW discharge periods, relative to nighttime TSW discharge periods. The experimental design of the current study used start times near dawn for day periods and near dusk for night periods.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Decoupled Active and Reactive Power Control without PLL Requirement for Differential Buck Converter

This paper presents a decoupled active and reactive power control for the differential buck converter. This control does not require phase locked loop (PLL) for synchronization. Also, it achieves active and reactive power control in a simple single control loop structure. The differential buck converter has the capability to compensate the double line frequency power ripple without relying on additional hardware. Particularly, the Common Mode (CM) operation is used for active double line frequency power ripple absorption. Whereas, the Differential Mode (DM) operation is used as an active and reactive power exchanging port between the converter and the grid at the point of common coupling (PCC). The motivation behind this paper proposal are: (i) to avoid PLL induced instabilities, especially, when connecting the differential buck converter with weak grid, and (ii) direct active and reactive power control for the differential buck in a single loop control. The theoretical analyses are verified with a 5 kW converter with only 50 μF decoupling capacitor connected to a weak grid.

Khan, Ahmad↗
DOE OSTI2021

Encoder–decoder neural network for solving the nonlinear Fokker–Planck–Landau collision operator in XGC

An encoder–decoder neural network has been used to examine the possibility for acceleration of a partial integro-differential equation, the Fokker–Planck–Landau collision operator. This is part of the governing equation in the massively parallel particle-in-cell code XGC, which is used to study turbulence in fusion energy devices. The neural network emphasizes physics-inspired learning, where it is taught to respect physical conservation constraints of the collision operator by including them in the training loss, along with the ℓ 2 loss. In particular, network architectures used for the computer vision task of semantic segmentation have been used for training. A penalization method is used to enforce the ‘soft’ constraints of the system and integrate error in the conservation properties into the loss function. During training, quantities representing the particle density, momentum and energy for all species of the system are calculated at each configuration vertex, mirroring the procedure in XGC. This simple training has produced a median relative loss, across configuration space, of the order of 10 –4 , which is low enough if the error is of random nature, but not if it is of drift nature in time steps. The run time for the current Picard iterative solver of the operator is O(n 2 ), where n is the number of plasma species. As the XGC1 code begins to attack problems including a larger number of species, the collision operator will become expensive computationally, making the neural network solver even more important, especially since its training only scales as O(n). Here, a wide enough range of collisionality has been considered in the training data to ensure the full domain of collision physics is captured. An advanced technique to decrease the losses further will be subject of a subsequent report. Eventual work will include expansion of the network to include multiple plasma species.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

TANTE: Time-adaptive operator learning via neural Taylor expansion

Operator learning for time-dependent partial differential equations (PDEs) has seen rapid progress in recent years, enabling efficient approximation of complex spatiotemporal dynamics. However, most existing methods rely on fixed time step sizes during rollout, which limits their ability to adapt to varying temporal complexity and often leads to error accumulation. In this work, we propose the Time-Adaptive Transformer with Neural Taylor Expansion (TANTE), a novel operator-learning framework that produces continuous-time predictions with adaptive step sizes. TANTE predicts future states by performing a Taylor expansion at the current state, where neural networks learn both the higher-order temporal derivatives and the local radius of convergence. This allows the model to dynamically adjust its rollout based on the local behavior of the solution, thereby reducing cumulative error and improving computational efficiency. We demonstrate the effectiveness of TANTE across a wide range of PDE benchmarks, achieving superior accuracy and adaptability compared to fixed-step baselines, delivering accuracy gains of 60-80 % and speed-ups of 30-40 % at inference time.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Spectral scheme for atomic structure calculations in density functional theory

In this study, we present a spectral scheme for atomic structure calculations in pseudopotential Kohn-Sham density functional theory. In particular, after applying an exponential transformation of the radial coordinates, we employ global polynomial interpolation on a Chebyshev grid, with derivative operators approximated using the Chebyshev differentiation matrix, and integrations using Clenshaw-Curtis quadrature. We demonstrate the accuracy and efficiency of the scheme through spin-polarized and unpolarized calculations for representative atoms, while considering local, semilocal, and hybrid exchange-correlation functionals. In particular, we find that $\mathcal{O}$(200) grid points are sufficient to achieve an accuracy of 1 microhartree in the eigenvalues for optimized norm conserving Vanderbilt pseudopotentials spanning the periodic table from atomic number Ζ = 1 to 83.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Learning functional priors and posteriors from data and physics

In this work, we develop a new Bayesian framework based on deep neural networks to be able to extrapolate in space-time using historical data and to quantify uncertainties arising from both noisy and gappy data in physical problems. Specifically, the proposed approach has two stages: (1) prior learning and (2) posterior estimation. At the first stage, we employ the physics-informed Generative Adversarial Networks (PI-GAN) to learn a functional prior either from a prescribed function distribution, e.g., Gaussian process, or from historical data and physics. At the second stage, we employ the Hamiltonian Monte Carlo (HMC) method to estimate the posterior in the latent space of PI-GANs. In addition, we use two different approaches to encode the physics: (1) automatic differentiation, used in the physicsinformed neural networks (PINNs) for scenarios with explicitly known partial differential equations (PDEs), and (2) operator regression using the deep operator network (DeepONet) for PDE-agnostic scenarios. We then test the proposed method for (1) meta-learning for one-dimensional regression, and forward/inverse PDE problems (combined with PINNs); (2) PDE-agnostic physical problems (combined with DeepONet), e.g., fractional diffusion as well as saturated stochastic (100-dimensional) flows in heterogeneous porous media; and (3) spatial-temporal regression problems, i.e., inference of a marine riser displacement field using experimental data from the Norwegian Deepwater Programme (NDP). The results demonstrate that the proposed approach can provide accurate predictions as well as uncertainty quantification given very limited scattered and noisy data, since historical data could be available to provide informative priors. In summary, the proposed method is capable of learning flexible functional priors, e.g., both Gaussian and non-Gaussian process, and can be readily extended to big data problems by enabling mini-batch training using stochastic HMC or normalizing flows since the latent space is generally characterized as low dimensional.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗