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DOE OSTI2023

Combining variational autoencoders and physical bias for improved microscopy data analysis *

Electron and scanning probe microscopy produce vast amounts of data in the form of images or hyperspectral data, such as electron energy loss spectroscopy or 4D scanning transmission electron microscope, that contain information on a wide range of structural, physical, and chemical properties of materials. To extract valuable insights from these data, it is crucial to identify physically separate regions in the data, such as phases, ferroic variants, and boundaries between them. In order to derive an easily interpretable feature analysis, combining with well-defined boundaries in a principled and unsupervised manner, here we present a physics augmented machine learning method which combines the capability of variational autoencoders to disentangle factors of variability within the data and the physics driven loss function that seeks to minimize the total length of the discontinuities in images corresponding to latent representations. Our method is applied to various materials, including NiO-LSMO, BiFeO 3 , and graphene. The results demonstrate the effectiveness of our approach in extracting meaningful information from large volumes of imaging data. The customized codes of the required functions and classes to develop phyVAE is available at https://github.com/arpanbiswas52/phy-VAE.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Physics-informed latent neural operator for real-time predictions of time-dependent parametric PDEs

Deep operator network (DeepONet) has shown significant promise as surrogate models for systems governed by partial differential equations (PDEs), enabling accurate mappings between infinite-dimensional function spaces. However, when applied to systems with high-dimensional input-output mappings arising from large numbers of spatial and temporal collocation points, these models often require heavily overparameterized networks, leading to long training times. Latent DeepONet addresses some of these challenges by introducing a two-step approach: first learning a reduced latent space using a separate model, followed by operator learning within this latent space. While efficient, this method is inherently data-driven and lacks mechanisms for incorporating physical laws, limiting its robustness and generalizability in data-scarce settings. Here, in this work, we propose PI-Latent-NO, a physics-informed latent neural operator framework that integrates governing physics directly into the learning process. Our architecture features two coupled DeepONets trained end-to-end: a Latent-DeepONet that learns a low-dimensional representation of the solution, and a Reconstruction-DeepONet that maps this latent representation back to the physical space. By embedding PDE constraints into the training via automatic differentiation, our method eliminates the need for labeled training data and ensures physics-consistent predictions. The proposed framework is both memory and compute-efficient, exhibiting near-constant scaling with problem size and demonstrating significant speedups over traditional physics-informed operator models. We validate our approach on a range of parametric PDEs, showcasing its accuracy, scalability, and suitability for real-time prediction in complex physical systems.

Latent representations↗

DOE OSTI2024

A Deep Learning-Driven Sampling Technique to Explore the Phase Space of an RNA Stem-Loop

The folding and unfolding of RNA stem-loops are critical biological processes; however, their computational studies are often hampered by the ruggedness of their folding landscape, necessitating long simulation times at the atomistic scale. Here, we adapted DeepDriveMD (DDMD), an advanced deep learning-driven sampling technique originally developed for protein folding, to address the challenges of RNA stem-loop folding. Although tempering- and order parameter-based techniques are commonly used for similar rare-event problems, the computational costs or the need for a priori knowledge about the system often present a challenge in their effective use. DDMD overcomes these challenges by adaptively learning from an ensemble of running MD simulations using generic contact maps as the raw input. DeepDriveMD enables on-the-fly learning of a low-dimensional latent representation and guides the simulation toward the undersampled regions while optimizing the resources to explore the relevant parts of the phase space. We showed that DDMD estimates the free energy landscape of the RNA stem-loop reasonably well at room temperature. Our simulation framework runs at a constant temperature without external biasing potential, hence preserving the information on transition rates, with a computational cost much lower than that of the simulations performed with external biasing potentials. Here, we also introduced a reweighting strategy for obtaining unbiased free energy surfaces and presented a qualitative analysis of the latent space. This analysis showed that the latent space captures the relevant slow degrees of freedom for the RNA folding problem of interest. Finally, throughout the manuscript, we outlined how different parameters are selected and optimized to adapt DDMD for this system. We believe this compendium of decision-making processes will help new users adapt this technique for the rare-event sampling problems of their interest.

Gupta, Ayush↗

DOE OSTI2025

Latent diffusion can map beam loss to two-dimensional phase-space projections

Beam loss monitors (BLMs) and beam current monitors (BCMs) are ubiquitous at particle accelerators around the world. These simple devices provide noninvasive high-level beam measurements but give no insight into the detailed 6D (𝑥,𝑦,𝑧,𝑝 𝑥 ,𝑝 𝑦 ,𝑝 𝑧 ) beam phase-space distributions or dynamics. We show that generative conditional latent diffusion models can learn intricate patterns to solve the extreme inverse problem of mapping waveforms of tens of BLMs or BCMs along an accelerator to detailed 2D projections of a charged particle beam’s 6D phase-space density. This transformational method can be used at any particle accelerator to transform simple noninvasive devices into detailed beam phase-space diagnostics. We demonstrate this concept via multiparticle simulations of the high-intensity beam in the kilometer-long Los Alamos Neutron Science Center linear proton accelerator.

43 PARTICLE ACCELERATORS↗

DOE OSTI2021

Outlier classification using autoencoders: application for fluctuation driven flows in fusion plasmas

Understanding the statistics of fluctuation driven flows in the boundary layer of magnetically confined plasmas is desired to accurately model the lifetime of the vacuum vessel components. Mirror Langmuir probes (MLPs) are a novel diagnostic that uniquely allow us to sample the plasma parameters on a time scale shorter than the characteristic time scale of their fluctuations. Sudden large-amplitude fluctuations in the plasma degrade the precision and accuracy of the plasma parameters reported by MLPs for cases in which the probe bias range is of insufficient amplitude. While some data samples can readily be classified as valid and invalid, we find that such a classification may be ambiguous for up to 40% of data sampled for the plasma parameters and bias voltages considered in this study. In this contribution, we employ an autoencoder (AE) to learn a low-dimensional representation of valid data samples. By definition, the coordinates in this space are the features that mostly characterize valid data. Ambiguous data samples are classified in this space using standard classifiers for vectorial data. In this way, we avoid defining complicated threshold rules to identify outliers, which require strong assumptions and introduce biases in the analysis. By removing the outliers that are identified in the latent low-dimensional space of the AE, we find that the average conductive and convective radial heat fluxes are between approximately 5% and 15% lower as when removing outliers identified by threshold values. For contributions to the radial heat flux due to triple correlations, the difference is up to 40%.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Toward Decoding the Relationship between Domain Structure and Functionality in Ferroelectrics via Hidden Latent Variables

Polarization switching mechanisms in ferroelectric materials are fundamentally linked to local domain structure and the presence of the structural defects, which both can act as nucleation and pinning centers and create local electrostatic and mechanical depolarization fields affecting wall dynamics. However, the general correlative mechanisms between domain structure and polarization dynamics are only weakly explored, precluding insight into the associated physical mechanisms. In this work, the correlation between local domain structures and switching behavior in ferroelectric materials is explored using convolutional encoder–decoder networks, enabling image to spectral (im2spec) and spectral to image (spec2im) translations via encoding of latent variables. The latter reflect the assumption that the relationship between domain structure and polarization switching is parsimonious, i.e., is based upon a small number of local mechanisms. The analysis of latent variables distributions and their real-space representations provides insight into the predictability of the local switching behavior and hence associated physical mechanisms. We further pose that the regions where these correlative relationships are violated, i.e., predictability of the polarization dynamics from domain structure is reduced, represent the obvious target for detailed studies, e.g., in the context of automated experiments. This approach provides a workflow to establish the presence of correlation between local spectral responses and local structure and can be universally applied to spectral imaging techniques such as piezoresponse force microscopy (PFM), scanning tunneling microscopy (STM) and spectroscopy, and electron energy loss spectroscopy (EELS) in scanning transmission electron microscopy (STEM).

36 MATERIALS SCIENCE↗

DOE OSTI2026

FunDiff: diffusion models over function spaces for physics-informed generative modeling

Recent advances in generative modeling-particularly diffusion models and flow matching-have been widely used for synthesizing discrete data such as images and videos. However, adapting these models to physical applications remains challenging, as the quantities of interest are continuous functions governed by complex physical laws. To address this, we introduce FunDiff, an efficient and robust framework for generative modeling in function spaces. FunDiff combines a latent diffusion process with a function autoencoder architecture to handle input functions with varying discretizations, generates continuous functions that can be evaluated at arbitrary locations, and seamlessly incorporate physical priors. These priors are enforced through architectural constraints or physics-informed loss functions, ensuring that generated samples satisfy fundamental physical laws. We theoretically establish minimax optimality guarantees for density estimation in function spaces, demonstrating that diffusion-based estimators achieve optimal convergence rates under suitable regularity conditions. We further demonstrate the practical effectiveness of FunDiff across diverse applications in fluid dynamics and solid mechanics. Empirical results indicate that our method can generate physically consistent samples with high fidelity to the target distribution, and exhibit robustness to noisy and low-resolution data.

Wang, Sifan [Yale University, New Haven, CT (Unite↗

DOE OSTI2026

Latent heat thermal energy storage performance maps enabling fast & accurate building energy simulations

Thermal energy storage (TES) using phase change materials (PCMs) has gained attention as an effective approach to manage energy demand fluctuations and shift peak building loads. PCM embedded heat exchangers (PCM-HXs) offer high energy storage density and low temperature variation during phase change, being suitable for load-shifting applications. However, this component is typically evaluated using computationally expensive methods, which present significant challenges when the ultimate goal is to assess the performance of PCM-HX integrated thermal energy storage systems in the full building context. In this paper, we present a methodology to generate highly accurate and computationally efficient PCM-HX performance maps which can be easily integrated into building energy simulation tools to analyze the feasibility of space conditioning systems with latent heat PCM-based TES. The performance maps are generated using a computationally efficient PCM-HX simulation tool based on a Generalized Resistance-Capacitance Model (GRCM) which can simulate arbitrary PCM-HXs with high accuracy and significantly less computational effort compared to full CFD simulations. The methodology was verified for a case study considering a 5-ton (~17.5 kW) air-to-water heat pump-thermal energy storage system (HP-TES), which was co-simulated in Modelica for a DOE prototype small-office building in Vienna, Austria, using Spawn of EnergyPlus™. The TES performance maps provided accurate predictions of PCM-HX behavior when used as Modelica component, with deviations within 2-4% while also achieving at least 103 computational time reduction. Leveraging this faster prediction capability, four PCMs with different melting temperatures for cooling (12°C, 16°C) and heating (31°C, 36°C) were assessed to investigate their impact on system performance. This work highlights the importance of robust PCM-HX models for efficient and high-fidelity building-level simulations, presenting new opportunities for advanced control strategy development and parametric analysis of TES configurations in a computationally efficient manner

Modelica Building Simulations↗

DOE OSTI2021

Internally cooled membrane-based absorber for dehumidification and water heating: Validated model and simulation study

This report presents a comprehensive model for advanced membrane-based absorber components accounting for three separate fluid streams, one of them providing internal cooling, with complex flow patterns. The model was implemented with various liquid desiccants and their properties (including LiCl, CaCl 2 , and [emim][OMS] ionic liquid [IL]). The model has been validated using data from two laboratory prototype absorbers, one with CaCl 2 as the working fluid and one with an IL as the working fluid. Entropy analysis was further carried out to verify the model and understand effect of internal cooling on the entropy variation of three fluid streams. The developed model and codes are expected to enable detailed configuration optimization and provide in-depth understanding of three-fluid heat and mass exchanger (HMX) performance. The paper also describes parametric studies of the HMX components in utilizing the latent heat removed in space cooling to heat water and numerically explores the unique benefit of its application in a semi-open absorption heat pump water heater. The results show that a single three-fluid HMX has the potential to achieve simultaneous dehumidification and water heating efficiently at cost effectiveness, particularly in hot and humid climates.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2026

Iterative HOMER with uncertainties

We present iHOMER, an iterative version of the HOMER method to extract Lund fragmentation functions from experimental data. Through iterations, we address the information gap between latent and observable phase spaces and systematically remove bias. To quantify uncertainties on the inferred weights, we use a combination of Bayesian neural networks and uncertainty-aware regression. We find that the combination of iterations and uncertainty quantification produces well-calibrated weights that accurately reproduce the data distribution. A parametric closure test shows that the iteratively learned fragmentation function is compatible with the true fragmentation function.

Butter, Anja [Heidelberg Univ. (Germany); Sorbonne↗

DOE OSTI2021

Bayesian learning of orthogonal embeddings for multi-fidelity Gaussian Processes

Uncertainty propagation in complex engineering systems often poses significant computational challenges related to modeling and quantifying probability distributions of model outputs, as those emerge as the result of various sources of uncertainty that are inherent in the system under investigation. Gaussian Processes regression (GPs) is a robust meta-modeling technique that allows for fast model prediction and exploration of response surfaces. Multi-fidelity variations of GPs further leverage information from cheap and low fidelity model simulations in order to improve their predictive performance on the high fidelity model. In order to cope with the high volume of data required to train GPs in high dimensional design spaces, a common practice is to introduce latent design variables that are typically projections of the original input space to a lower dimensional subspace, and therefore substitute the problem of learning the initial high dimensional mapping, with that of training a GP on a low dimensional space. Here in this paper, we present a Bayesian approach to identify optimal transformations that map the input points to low dimensional latent variables. The \projection" mapping consists of an orthonormal matrix that is considered a priori unknown and needs to be inferred jointly with the GP parameters, conditioned on the available training data. The proposed Bayesian inference scheme relies on a two-step iterative algorithm that samples from the marginal posteriors of the GP parameters and the projection matrix respectively, both using Markov Chain Monte Carlo (MCMC) sampling. In order to take into account the orthogonality constraints imposed on the orthonormal projection matrix, a Geodesic Monte Carlo sampling algorithm is employed, that is suitable for exploiting probability measures on manifolds. We extend the proposed framework to multi-fidelity models using GPs including the scenarios of training multiple outputs together. We validate our framework on three synthetic problems with a known lower-dimensional subspace. The benefits of our proposed framework, are illustrated on the computationally challenging aerodynamic optimization of a last-stage blade for an industrial gas turbine, where we study the effect of an 85-dimensional shape parameterization of a three-dimensional airfoil on two output quantities of interest, specifically on the aerodynamic efficiency and the degree of reaction

42 ENGINEERING↗

DOE OSTI2023

Multi-objective, robust constraints enforced global topology optimizer for optical devices

A method for optimization of photonic devices is disclosed. The method includes receiving a set of unconstrained latent variables; mapping the set of unconstrained latent variables to a constrained space to generate a constrained device; calculating the permittivity across each element of the constrained device; determining a permittivity-constrained width gradient based at least partially on the permittivity across each element; and optimizing the set of unconstrained latent variables by at least partially using the permittivity-constrained width gradient.

Fan, Jonathan↗

DOE OSTI2023

Optimizing training trajectories in variational autoencoders via latent Bayesian optimization approach *

Unsupervised and semi-supervised ML methods such as variational autoencoders (VAE) have become widely adopted across multiple areas of physics, chemistry, and materials sciences due to their capability in disentangling representations and ability to find latent manifolds for classification and/or regression of complex experimental data. Like other ML problems, VAEs require hyperparameter tuning, e.g. balancing the Kullback–Leibler and reconstruction terms. However, the training process and resulting manifold topology and connectivity depend not only on hyperparameters, but also their evolution during training. Because of the inefficiency of exhaustive search in a high-dimensional hyperparameter space for the expensive-to-train models, here we have explored a latent Bayesian optimization (zBO) approach for the hyperparameter trajectory optimization for the unsupervised and semi-supervised ML and demonstrated for joint-VAE with rotational invariances. We have demonstrated an application of this method for finding joint discrete and continuous rotationally invariant representations for modified national institute of standards and technology database (MNIST) and experimental data of a plasmonic nanoparticles material system. The performance of the proposed approach has been discussed extensively, where it allows for any high dimensional hyperparameter trajectory optimization of other ML models.

42 ENGINEERING↗

DOE OSTI2024

Resolving Nonequilibrium Shape Variations among Millions of Gold Nanoparticles

Nanoparticles, exhibiting functionally relevant structural heterogeneity, are at the forefront of cutting-edge research. Now, high-throughput single-particle imaging (SPI) with X-ray free-electron lasers (XFELs) creates opportunities for recovering the shape distributions of millions of particles that exhibit functionally relevant structural heterogeneity. To realize this potential, three challenges have to be overcome: (1) simultaneous parametrization of structural variability in real and reciprocal spaces; (2) efficiently inferring the latent parameters of each SPI measurement; (3) scaling up comparisons between 10 5 structural models and 10 6 XFEL-SPI measurements. Here, we describe how we overcame these three challenges to resolve the nonequilibrium shape distributions within millions of gold nanoparticles imaged at the European XFEL. These shape distributions allowed us to quantify the degree of asymmetry in these particles, discover a relatively stable “shape envelope” among nanoparticles, discern finite-size effects related to shape-controlling surfactants, and extrapolate nanoparticles’ shapes to their idealized thermodynamic limit. Ultimately, these demonstrations show that XFEL SPI can help transform nanoparticle shape characterization from anecdotally interesting to statistically meaningful.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

A system identification approach for non-intrusive reduced order modeling of radiation-induced photocurrents

In this study, development of compact photocurrent models is currently dominated by analytical techniques that rely on physical assumptions to render the governing equations solvable in a closed form. Violation of these assumptions can reduce the accuracy of the models and/or limit their scope. In this paper we show that system identification of nonlinear state-space systems can serve as an alternative numerical basis for non-intrusive reduced order modeling of photocurrent effects. To that end we develop a compact gray box photocurrent model (GBPM) by using a state-space representation with a low-dimensional latent state equation that mimics a mathematical model for the response of an idealized class of devices to ionizing radiation. In so doing we obtain a model that learns the dynamics of a quantity of interest directly from its measurements without requiring snapshots of the internal device state or its discretized model, and can be inferred from very small data sets. To demonstrate the approach we train the GBPM using a small experimental data set for a Z5236 Zener diode and a small synthetic data set obtained by simulating a synthetic pn-junction device. We then compare the GBPMs with black box models trained on the same data and show that performance of the latter is limited by the size of the data set, while the former are able to achieve excellent performance in both the reproductive and the predictive regimes.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Ultrafast x-ray imaging of coherently controlled molecular dynamics in real space and time

Coherent control aims to manipulate chemical processes on the latent length and timescales of atoms and bonds, scales that are intrinsic to molecular dynamics but not directly resolved by most experimental probes. As a result, existing coherent-control experiments, which overwhelmingly rely on spectroscopic observables, leave a crucial blind spot: the direct, real-space recovery of all atomic and molecular rearrangements in response to coherently controlled excitations. Here, we overcome this limitation by integrating a Tannor-Kosloff-Rice pump-control-probe scheme with ultrafast X-ray scattering to capture snapshots of the wavepacket motion in a benchmark molecular system. We demonstrate this by photoexciting diatomic iodine vapor with a visible pump pulse, selectively steering the wavepacket toward ground-state recombination or dissociative pathways with a time-delayed near-IR control pulse, and recording the dynamics with angstrom and femtosecond precision with an ultrashort hard X-ray probe pulse. By comparing these structural observations with numerical solutions of the time-dependent Schrödinger equation, we reveal how coherent control actively reshapes the molecular charge density distribution. Our results pave the way for leveraging structural feedback as a control handle and provide a fundamental microscopic visualization of quantum decoherence and energy redistribution at the atomic level.

Hopper, Thomas R. [SLAC National Accelerator Labor↗

DOE OSTI2023

Neural embedding: learning the embedding of the manifold of physics data

In this paper, we present a method of embedding physics data manifolds with metric structure into lower dimensional spaces with simpler metrics, such as Euclidean and Hyperbolic spaces. We then demonstrate that it can be a powerful step in the data analysis pipeline for many applications. Using progressively more realistic simulated collisions at the Large Hadron Collider, we show that this embedding approach learns the underlying latent structure. With the notion of volume in Euclidean spaces, we provide for the first time a viable solution to quantifying the true search capability of model agnostic search algorithms in collider physics (i.e. anomaly detection). Finally, we discuss how the ideas presented in this paper can be employed to solve many practical challenges that require the extraction of physically meaningful representations from information in complex high dimensional datasets.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Design and performance assessment of a dual-mode latent thermal storage integrated heat pump across multiple climate zones

The electrification of space cooling and heating systems risks overloading the existing electrical grid during peak hours. Heat pumps integrated with thermal energy storage (HP-TES) offer a promising solution by shifting peak loads to off-peak hours, reducing grid strains. This work presents the design and assessment of a dual-mode HP-TES that uses a single 22°C phase-change material (PCM) as a heat source or sink in heating and cooling modes, respectively. Performance assessment was conducted using Modelica-based transient models, and full-year simulations were conducted across eight US climate zones using typical weather data. Two HP-TES performance metrics: peak energy reduction and recharge energy increases, were defined by comparing HP-TES energy consumption with base HP peak consumptions. Annual heating demand reductions (40–65%) exceeded cooling demand reductions (15–20%) due to the elimination of peak-hour backup heating. Cooling mode recharge energy requirements (0–10%) were reduced in locations with lower summer nighttime temperatures, while heating recharge requirements were lower than the high base-peak energy demand from backup heating. Simplified rapid methods that were 10 7 times faster than annual simulations were developed to predict seasonal cooling and heating energy reductions, and recharge energy requirements, with maximum deviations of ±2.5% and ±3.5% points. These methods enabled rapid parametric studies that identified optimal location-specific PCM temperatures between 22°C and 27°C, highlighting the need to consider both discharge and recharge energy requirements to achieve sustainable, energy-efficient peak load shifting across various climate zones.

25 ENERGY STORAGE↗