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DOE OSTI2025

AutoTandemML: Active Learning Enhanced Tandem Neural Networks for Inverse Design Problems

Inverse design in science and engineering involves determining optimal design parameters that achieve desired performance outcomes, a process often hindered by the complexity and high dimensionality of design spaces, leading to significant computational costs. To tackle this challenge, we propose a novel hybrid approach that combines active learning with Tandem Neural Networks to enhance the efficiency and effectiveness of solving inverse design problems. Active learning allows to selectively sample the most informative data points, reducing the required dataset size without compromising accuracy. We investigate this approach using three benchmark problems: airfoil inverse design, photonic surface inverse design, and scalar boundary condition reconstruction in diffusion partial differential equations. We demonstrate that integrating active learning with Tandem Neural Networks outperforms standard approaches across the benchmark suite, achieving better accuracy with fewer training samples.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

AIVT: Inference of turbulent thermal convection from measured 3D velocity data by physics-informed Kolmogorov-Arnold networks

We propose the artificial intelligence velocimetry-thermometry (AIVT) method to reconstruct a continuous and differentiable representation of the temperature and velocity in turbulent convection from measured three-dimensional (3D) velocity data. AIVT is based on physics-informed Kolmogorov-Arnold networks and trained by optimizing a loss function that minimizes residuals of the velocity data, boundary conditions, and governing equations. We apply AIVT to a set of simultaneously measured 3D temperature and velocity data of Rayleigh-Bénard convection, obtained by combining particle image thermometry and Lagrangian particle tracking. This enables us to directly compare machine learning results to true volumetric, simultaneous temperature and velocity measurements. We demonstrate that AIVT can reconstruct and infer continuous, instantaneous velocity and temperature fields and their gradients from sparse experimental data at a high resolution, providing an additional approach for understanding thermal turbulence.

Science & Technology - Other Topics↗

NASA NTRS1993

A new approach for designing self-organizing systems and application to adaptive control

There is tremendous interest in the design of intelligent machines capable of autonomous learning and skillful performance under complex environments. A major task in designing such systems is to make the system plastic and adaptive when presented with new and useful information and stable in response to irrelevant events. A great body of knowledge, based on neuro-physiological concepts, has evolved as a possible solution to this problem. Adaptive resonance theory (ART) is a classical example under this category. The system dynamics of an ART network is described by a set of differential equations with nonlinear functions. An approach for designing self-organizing networks characterized by nonlinear differential equations is proposed.

Ramamoorthy, P. A.↗

DOE OSTI2022

Neural network reconstruction of the dense matter equation of state from neutron star observables

The Equation of State (EoS) of strongly interacting cold and hot ultra-dense QCD matter remains a major challenge in the field of nuclear astrophysics. With the advancements in measurements of neutron star masses, radii, and tidal deformabilities, from electromagnetic and gravitational wave observations, neutron stars play an important role in constraining the ultra-dense QCD matter EoS. Here, in this work, we present a novel method that exploits deep learning techniques to reconstruct the neutron star EoS from mass-radius (M-R) observations. We employ neural networks (NNs) to represent the EoS in a model-independent way, within the range of ~1-7 times the nuclear saturation density. The unsupervised Automatic Differentiation (AD) framework is implemented to optimize the EoS, so as to yield through TOV equations, an M-R curve that best fits the observations. We demonstrate that this method works by rebuilding the EoS on mock data, i.e., mass-radius pairs derived from a randomly generated polytropic EoS. The reconstructed EoS fits the mock data with reasonable accuracy, using just 11 mock M-R pairs observations, close to the current number of actual observations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2019

Isotope effects in liquid water via deep potential molecular dynamics

A comprehensive microscopic understanding of ambient liquid water is a major challenge for ab initio simulations as it simultaneously requires an accurate quantum mechanical description of the underlying potential energy surface (PES) as well as extensive sampling of configuration space. Due to the presence of light atoms (e.g. 𝐻 or 𝐷), nuclear quantum fluctuations lead to observable changes in the structural properties of liquid water (e.g. isotope effects), and therefore provide yet another challenge for ab initio approaches. In this work, we demonstrate that the combination of dispersion-inclusive hybrid density functional theory (DFT), the Feynman discretised path-integral (PI) approach, and machine learning (ML) constitutes a versatile ab initio based framework that enables extensive sampling of both thermal and nuclear quantum fluctuations on a quite accurate underlying PES. In particular, we employ the recently developed deep potential molecular dynamics (DPMD) model – a neural-network representation of the ab initio PES – in conjunction with a PI approach based on the generalised Langevin equation (PIGLET) to investigate how isotope effects influence the structural properties of ambient liquid 𝐻⁢2⁢𝑂 and 𝐷⁢2⁢𝑂. Through a detailed analysis of the interference differential cross sections as well as several radial and angular distribution functions, we demonstrate that this approach can furnish a semi-quantitative prediction of these subtle isotope effects.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Applying Quantum Computing to Simulate Power System Dynamics

Power system dynamics are generally modeled by high dimensional nonlinear differential-algebraic equations due to a large number of generators, loads, and transmission lines. Thus, its computational complexity grows exponentially with the system size. This paper demonstrates the potential use of quantum computing algorithms to model the power system dynamics. Leveraging a symbolic programming framework, we equivalently convert the power system dynamics’ differential algebraic equations (DAEs) into ordinary differential equations (ODEs), where the data of the state vector can be encoded into quantum computers via amplitude encoding. The system's nonlinearity is captured by Taylor polynomial expansion, the quantum state tensor, and Hamiltonian simulation, whereas state variables can be updated by a quantum linear equation solver. Our results show that quantum computing can simulate the dynamics of the power system with high accuracy, whereas its complexity is polynomial in the logarithm of the system dimension. Our work also illustrates the use of scientific machine learning tools for implementing scientific computing concepts, e.g., Taylor expansion, DAEs/ODEs transform, and quantum computing solver, in the field of power engineering.

Tran, Huynh↗

DOE OSTI2022

Geochemistry and Multiomics Data Differentiate Streams in Pennsylvania Based on Unconventional Oil and Gas Activity

Unconventional oil and gas (UOG) extraction is increasing exponentially around the world, as new technological advances have provided cost-effective methods to extract hard-to-reach hydrocarbons. While UOG has increased the energy output of some countries, past research indicates potential impacts in nearby stream ecosystems as measured by geochemical and microbial markers. Here, we utilized a robust data set that combines 16S rRNA gene amplicon sequencing (DNA), metatranscriptomics (RNA), geochemistry, and trace element analyses to establish the impact of UOG activity in 21 sites in northern Pennsylvania. These data were also used to design predictive machine learning models to determine the UOG impact on streams. We identified multiple biomarkers of UOG activity and contributors of antimicrobial resistance within the order Burkholderiales. Furthermore, we identified expressed antimicrobial resistance genes, land coverage, geochemistry, and specific microbes as strong predictors of UOG status. Of the predictive models constructed (n = 30), 15 had accuracies higher than expected by chance and area under the curve values above 0.70. The supervised random forest models with the highest accuracy were constructed with 16S rRNA gene profiles, metatranscriptomics active microbial composition, metatranscriptomics active antimicrobial resistance genes, land coverage, and geochemistry (n = 23). The models identified the most important features within those data sets for classifying UOG status. These findings identified specific shifts in gene presence and expression, as well as geochemical measures, that can be used to build robust models to identify impacts of UOG development.

16S rRNA↗

DOE OSTI2024

Fast neutron leakage spectra of the EUCLID experiment

Special nuclear material in sub-critical and critical configurations measured in integral experiments are important for validation and adjustment of nuclear data. Many different evaluations of nuclear data exist, and these different evaluations can provide different values for individual cross sections that vary due to the uncertainties in differential experiments or lack of such data. For integral experiments, differences in these individual cross sections can have compensating errors, which lead to the same answer. One example of this is the Jezebel critical assembly, where k eff of the system is correctly computed by both ENDF/B-VIII.0 and JEFF-3.3, despite having substantially different underlying evaluated values for specific reactions (such as elastic and inelastic cross sections). To reduce compensating errors in nuclear data, the Experiments Underpinned by Computational Learning for Improvements in Nuclear Data (EUCLID) project has utilized machine learning to design a set of sub-critical and critical experiments. These experiments include slab- and cube-like configurations of 239 Pu in the form of the ZPPR plates. Six different responses were measured on a total of thirteen different configurations. One of these responses, the neutron leakage spectrum, was measured using an EJ301D detector. Finally, the results of the neutron leakage spectra show good agreement (within 1–2 σ ) with the expected spectrum from simulations and will be used in the subsequent nuclear data adjustment done by the EUCLID team.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2022

Characterization of Acoustic Emissions From Analogue Rocks Using Sparse Regression‐DMDc

Abstract Moisture loss in rock is known to generate acoustic emissions (AE). Phenomena that result in AE during drying are related to the movement of fluids through the pores and induced‐cracks that arise from differential mineral shrinkage, especially in clay‐bearing rock. AE from the movement of fluids occurs from the reconfiguration of fluid interfaces during drying, while AE from mineral shrinkage involves the debonding within or between minerals. Here, analogue rock samples were used to examine the differences in the AE signatures when one or both AE source‐types are present. An unsupervised sparse regression model, Dynamic Mode Decomposition with control, that extends Dynamic Mode Decomposition is used to characterize the AE signals recorded during the drying of porous analogue rock samples fabricated with ordinary Portland cement, with and without clay. This method can effectively and accurately reconstruct acoustic signals emitted from samples that only experience moisture loss without cracking. However, the method struggles to reconstruct signals from samples with intricate crack networks that formed during drying because AE generating mechanisms can emit contemporaneously, and the resulting waves propagate through drying‐induced cracks that can lead to multiple internal reflections. Thus, the differential reconstruction accuracy of time series generated by different underlying physical processes provides a robust filter for reducing large data catalogs. In general, both dynamics and sparse initiating events are learned directly from data and this method exposes a data hierarchy based on the complexity of the intrinsic dynamics.

58 GEOSCIENCES↗

DOE OSTI2025

Accelerating phase field simulations through a hybrid adaptive Fourier neural operator with U-net backbone

Prolonged contact between a corrosive liquid and metal alloys can cause progressive dealloying. For one such process as liquid-metal dealloying (LMD), phase field models have been developed to understand the mechanisms leading to complex morphologies. However, the LMD governing equations in these models often involve coupled non-linear partial differential equations (PDE), which are challenging to solve numerically. In particular, numerical stiffness in the PDEs requires an extremely refined time step size (on the order of 10 -12 s or smaller). This computational bottleneck is especially problematic when running LMD simulation until a late time horizon is required. This motivates the development of surrogate models capable of leaping forward in time, by skipping several consecutive time steps at-once. In this paper, we propose a U-shaped adaptive Fourier neural operator (U-AFNO), a machine learning (ML) based model inspired by recent advances in neural operator learning. U-AFNO employs U-Nets for extracting and reconstructing local features within the physical fields, and passes the latent space through a vision transformer (ViT) implemented in the Fourier space (AFNO). We use U-AFNOs to learn the dynamics of mapping the field at a current time step into a later time step. We also identify global quantities of interest (QoI) describing the corrosion process (e.g., the deformation of the liquid-metal interface, lost metal, etc.) and show that our proposed U-AFNO model is able to accurately predict the field dynamics, in spite of the chaotic nature of LMD. Most notably, our model reproduces the key microstructure statistics and QoIs with a level of accuracy on par with the high-fidelity numerical solver, while achieving a significant 11, 200 × speed-up on a high-resolution grid when comparing the computational expense per time step. Finally, we also investigate the opportunity of using hybrid simulations, in which we alternate forward leaps in time using the U-AFNO with high-fidelity time stepping. We demonstrate that while advantageous for some surrogate model design choices, our proposed U-AFNO model in fully auto-regressive settings consistently outperforms hybrid schemes.

36 MATERIALS SCIENCE↗

DOE OSTI2023

A data-driven method for modelling dissipation rates in stratified turbulence

We present a deep probabilistic convolutional neural network (PCNN) model for predicting local values of small-scale mixing properties in stratified turbulent flows, namely the dissipation rates of turbulent kinetic energy and density variance, $\varepsilon$ and $\chi$ . Inputs to the PCNN are vertical columns of velocity and density gradients, motivated by data typically available from microstructure profilers in the ocean. The architecture is designed to enable the model to capture several characteristic features of stratified turbulence, in particular the dependence of small-scale isotropy on the buoyancy Reynolds number $Re_b:=\varepsilon /(\nu N^2)$ , where $\nu$ is the kinematic viscosity and $N$ is the background buoyancy frequency, the correlation between suitably locally averaged density gradients and turbulence intensity and the importance of capturing the tails of the probability distribution functions of values of dissipation. Empirically modified versions of commonly used isotropic models for $\varepsilon$ and $\chi$ that depend only on vertical derivatives of density and velocity are proposed based on the asymptotic regimes $Re_b\ll 1$ and $Re_b\gg 1$ , and serve as an instructive benchmark for comparison with the data-driven approach. When trained and tested on a simulation of stratified decaying turbulence which accesses a range of turbulent regimes (associated with differing values of $Re_b$ ), the PCNN outperforms assumptions of isotropy significantly as $Re_b$ decreases, and additionally demonstrates improvements over the fitted empirical models. A differential sensitivity analysis of the PCNN facilitates a comparison with the theoretical models and provides a physical interpretation of the features enabling it to make improved predictions.

42 ENGINEERING↗

DOE OSTI2022

Discovering hidden geothermal signatures using non-negative matrix factorization with customized k-means clustering

Discovery of hidden geothermal resources is challenging. It requires the mining of large datasets with diverse data attributes representing subsurface hydrogeological and geothermal conditions. The commonly used play fairway analysis approach typically incorporates subject-matter expertise to analyze regional data to estimate geothermal characteristics and favorability. We demonstrate an alternative approach based on machine learning (ML) to process a geothermal dataset from southwest New Mexico (SWNM). The study region includes low- and medium-temperature hydrothermal systems. Several of these systems are not well characterized because of insufficient existing data and limited past explorative work. This study discovers hidden patterns and relations in the SWNM geothermal dataset to improve our understanding of the regional hydrothermal conditions and energy-production favorability. This understanding is obtained by applying an unsupervised ML algorithm based on non-negative matrix factorization coupled with customized k-means clustering (NMFk). NMFk can automatically identify (1) hidden signatures characterizing analyzed datasets, (2) the optimal number of these signatures, (3) the dominant data attributes associated with each signature, and (4) the spatial distribution of the extracted signatures. Here, in this study, NMFk is applied to analyze 18 geological, geophysical, hydrogeological, and geothermal attributes at 44 locations in SWNM. Using NMFk, we find data patterns and identify the spatial associations of hydrothermal signatures within two physiographic provinces (Colorado Plateau and Basin and Range) and two sub-regions of these provinces (the Mogollon-Datil volcanic field and the Rio Grande rift) in SWNM. The ML algorithm extracted five hydrothermal signatures in the SWNM datasets that differentiate between low (<90°C) and medium (90-150°C)-temperature hydrothermal systems. The algorithm also suggests that the Rio Grande rift and northern Mogollon-Datil volcanic field are the most favorable regions for future geothermal resource discovery. NMFk also identified critical attributes to identify medium-temperature hydrothermal systems in the study area. The resulting NMFk model can be applied to predict geothermal conditions and their uncertainties at new SWNM locations based on limited data from unexplored regions. The code to execute the performed analyses as well as the corresponding data can be found at https://github.com/SmartTensors/GeoThermalCloud.jl.

15 GEOTHERMAL ENERGY↗

DOE OSTI2023

Embedding hard physical constraints in neural network coarse-graining of three-dimensional turbulence

In recent years, deep learning approaches have shown much promise in modeling complex systems in the physical sciences. A major challenge in deep learning of partial differential equations is enforcing physical constraints and boundary conditions. In this work, we propose a general framework to directly embed the notion of an incompressible fluid into convolutional neural networks, and apply this to coarse-graining of turbulent flow. These physics-embedded neural networks leverage interpretable strategies from numerical methods and computational fluid dynamics to enforce physical laws and boundary conditions by taking advantage the mathematical properties of the underlying equations. Here, we demonstrate results on three-dimensional fully developed turbulence, showing that this technique drastically improves local conservation of mass, without sacrificing performance according to several other metrics characterizing the fluid flow.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Thermal property characterization of phase change materials in building applications: A systematic review of fundamentals, recent progress, and future directions

Phase change materials (PCMs) can reduce building peak loads and enable demand-responsive thermal energy storage (TES), but their deployment depends on reliable measurement and interpretation of thermal properties across laboratory, intermediate, and application scales. Here, this review systematically examines characterization methods, testing protocols, and recent advances for neat PCMs and PCM composites, emphasizing thermal conductivity, enthalpy-related properties (phase change temperature, latent heat, specific heat), and cycling stability. For thermal conductivity, we compare steady-state and transient techniques and note limitations when phase transition and contact resistance affect measurements. For enthalpy–temperature characterization, we discuss differential scanning calorimetry together with intermediate- and bulk-scale methods, including T-history, heat flow meter testing, and three-layer calorimetry (3LC), to generate application-relevant enthalpy–temperature profiles. Cycling stability is organized into four experimental families: thermoelectric–air, fully thermoelectric, water-bath, and in situ chamber approaches, with attention to separating reversible supercooling from true degradation such as phase segregation. We highlight emerging noncontact diagnostics, including infrared thermography and embedded sensing, for spatially resolved validation and multiscale interpretation. Finally, we review the growing use of AI and machine learning for property prediction, inverse characterization from experimental signals, and real-time state estimation in building-integrated TES. Key needs include harmonized protocols, interlaboratory benchmarking, uncertainty reporting, and metadata-rich datasets to accelerate reproducible PCM qualification for grid-flexible buildings.

AI↗

DOE OSTI2018

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Hejre, we introduce physics-informed neural networks – neural networks that are trained to solve supervised learning tasks while respecting any given laws of physics described by general nonlinear partial differential equations. In this work, we present our developments in the context of solving two main classes of problems: data-driven solution and data-driven discovery of partial differential equations. Depending on the nature and arrangement of the available data, we devise two distinct types of algorithms, namely continuous time and discrete time models. The first type of models forms a new family of data-efficient spatio-temporal function approximators, while the latter type allows the use of arbitrarily accurate implicit Runge–Kutta time stepping schemes with unlimited number of stages. Moreover, the effectiveness of the proposed framework is demonstrated through a collection of classical problems in fluids, quantum mechanics, reaction–diffusion systems, and the propagation of nonlinear shallow-water waves.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Characterization of partial wetting by CMAS droplets using multiphase many-body dissipative particle dynamics and data-driven discovery based on PINNs

The molten sand that is a mixture of calcia, magnesia, alumina and silicate, known as CMAS, is characterized by its high viscosity, density and surface tension. The unique properties of CMAS make it a challenging material to deal with in high-temperature applications, requiring innovative solutions and materials to prevent its buildup and damage to critical equipment. Here, we use multiphase many-body dissipative particle dynamics simulations to study the wetting dynamics of highly viscous molten CMAS droplets. The simulations are performed in three dimensions, with varying initial droplet sizes and equilibrium contact angles. We propose a parametric ordinary differential equation (ODE) that captures the spreading radius behaviour of the CMAS droplets. The ODE parameters are then identified based on the physics-informed neural network (PINN) framework. Subsequently, the closed-form dependency of parameter values found by the PINN on the initial radii and contact angles are given using symbolic regression. Finally, we employ Bayesian PINNs (B-PINNs) to assess and quantify the uncertainty associated with the discovered parameters. In brief, this study provides insight into spreading dynamics of CMAS droplets by fusing simple parametric ODE modelling and state-of-the-art machine-learning techniques.

Mechanics↗

DOE OSTI2020

Machine learning and serving of discrete field theories

A method for machine learning and serving of discrete field theories in physics is developed. The learning algorithm trains a discrete field theory from a set of observational data on a spacetime lattice, and the serving algorithm uses the learned discrete field theory to predict new observations of the field for new boundary and initial conditions. The approach of learning discrete field theories overcomes the difficulties associated with learning continuous theories by artificial intelligence. The serving algorithm of discrete field theories belongs to the family of structure-preserving geometric algorithms, which have been proven to be superior to the conventional algorithms based on discretization of differential equations. The effectiveness of the method and algorithms developed is demonstrated using the examples of nonlinear oscillations and the Kepler problem. In particular, the learning algorithm learns a discrete field theory from a set of data of planetary orbits similar to what Kepler inherited from Tycho Brahe in 1601, and the serving algorithm correctly predicts other planetary orbits, including parabolic and hyperbolic escaping orbits, of the solar system without learning or knowing Newton’s laws of motion and universal gravitation. The proposed algorithms are expected to be applicable when the effects of special relativity and general relativity are important.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Data-driven surrogates for high dimensional models using Gaussian process regression on the Grassmann manifold

This paper introduces a surrogate modeling scheme based on Grassmannian manifold learning to be used for cost-efficient predictions of high-dimensional stochastic systems. The method exploits subspace-structured features of each solution by projecting it onto a Grassmann manifold. This point-wise linear dimensionality reduction harnesses the structural information to assess the similarity between solutions at different points in the input parameter space. The method utilizes a solution clustering approach in order to identify regions of the parameter space over which solutions are sufficiently similarly such that they can be interpolated on the Grassmannian. In this clustering, the reduced-order solutions are partitioned into disjoint clusters on the Grassmann manifold using the eigen-structure of properly defined Grassmannian kernels and, the Karcher mean of each cluster is estimated. Then, the points in each cluster are projected onto the tangent space with origin at the corresponding Karcher mean using the exponential mapping. For each cluster, a Gaussian process regression model is trained that maps the input parameters of the system to the reduced solution points of the corresponding cluster projected onto the tangent space. Using this Gaussian process model, the full-field solution can be efficiently predicted at any new point in the parameter space. In certain cases, the solution clusters will span disjoint regions of the parameter space. In such cases, for each of the solution clusters we utilize a second, density-based spatial clustering to group their corresponding input parameter points in the Euclidean space. The proposed method is applied to two numerical examples. Here, the first is a nonlinear stochastic ordinary differential equation with uncertain initial conditions where the surrogate is used to predict the time history solution. The second involves modeling of plastic deformation in a model amorphous solid using the Shear Transformation Zone theory of plasticity, where the proposed surrogate is used to predict the full strain field of a material specimen under large shear strains.

42 ENGINEERING↗