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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Local Noether theorem for quantum lattice systems and topological invariants of gapped states

Here, we study generalizations of the Berry phase for quantum lattice systems in arbitrary dimensions. For a smooth family of gapped ground states in d dimensions, we define a closed d + 2-form on the parameter space, which generalizes the curvature of the Berry connection. Its cohomology class is a topological invariant of the family. When the family is equivariant under the action of a compact Lie group G, topological invariants take values in the equivariant cohomology of the parameter space. These invariants unify and generalize the Hall conductance and the Thouless pump. A key role in these constructions is played by a certain differential graded Fréchet–Lie algebra attached to any quantum lattice system. As a by-product, we describe ambiguities in charge densities and conserved currents for arbitrary lattice systems with rapidly decaying interactions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Geometry-complete perceptron networks for 3D molecular graphs

Abstract Motivation The field of geometric deep learning has recently had a profound impact on several scientific domains such as protein structure prediction and design, leading to methodological advancements within and outside of the realm of traditional machine learning. Within this spirit, in this work, we introduce GCPNet, a new chirality-aware SE(3)-equivariant graph neural network designed for representation learning of 3D biomolecular graphs. We show that GCPNet, unlike previous representation learning methods for 3D biomolecules, is widely applicable to a variety of invariant or equivariant node-level, edge-level, and graph-level tasks on biomolecular structures while being able to (1) learn important chiral properties of 3D molecules and (2) detect external force fields. Results Across four distinct molecular-geometric tasks, we demonstrate that GCPNet’s predictions (1) for protein–ligand binding affinity achieve a statistically significant correlation of 0.608, more than 5%, greater than current state-of-the-art methods; (2) for protein structure ranking achieve statistically significant target-local and dataset-global correlations of 0.616 and 0.871, respectively; (3) for Newtownian many-body systems modeling achieve a task-averaged mean squared error less than 0.01, more than 15% better than current methods; and (4) for molecular chirality recognition achieve a state-of-the-art prediction accuracy of 98.7%, better than any other machine learning method to date. Availability and implementation The source code, data, and instructions to train new models or reproduce our results are freely available at https://github.com/BioinfoMachineLearning/GCPNet.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

SIDDA: SInkhorn Dynamic Domain Adaptation

Modern neural networks (NNs) often do not generalize well in the presence of a "covariate shift"; that is, in situations where the training and test data distributions differ, but the conditional distribution of classification labels remains unchanged. In such cases, NN generalization can be reduced to a problem of learning more domain-invariant features. Domain adaptation (DA) methods include a range of techniques aimed at achieving this; however, these methods have struggled with the need for extensive hyperparameter tuning, which then incurs significant computational costs. In this work, we introduce SIDDA, an out-of-the-box DA training algorithm built upon the Sinkhorn divergence, that can achieve effective domain alignment with minimal hyperparameter tuning and computational overhead. We demonstrate the efficacy of our method on multiple simulated and real datasets of varying complexity, including simple shapes, handwritten digits, and real astronomical observations. SIDDA is compatible with a variety of NN architectures, and it works particularly well in improving classification accuracy and model calibration when paired with equivariant neural networks (ENNs). We find that SIDDA enhances the generalization capabilities of NNs, achieving up to a ≈40% improvement in classification accuracy on unlabeled target data. We also study the efficacy of DA on ENNs with respect to the varying group orders of the dihedral group DN, and find that the model performance improves as the degree of equivariance increases. Finally, we find that SIDDA enhances model calibration on both source and target data--achieving over an order of magnitude improvement in the ECE and Brier score. SIDDA's versatility, combined with its automated approach to domain alignment, has the potential to advance multi-dataset studies by enabling the development of highly generalizable models.

Pandya, Sneh [Northeastern U.]↗
DOE OSTI2023

Densely Connected G-invariant Deep Neural Networks with Signed Permutation Representations

We introduce and investigate, for finite groups G, G-invariant deep neural network (GDNN) architectures with ReLU activation that are densely connected- i.e., include all possible skip connections. In contrast to other G-invariant architectures in the literature, the preactivations of theG-DNNs presented here are able to transform by signed permutation representations (signed perm-reps) of G. Moreover, the individual layers of the G-DNNs are not required to be G-equivariant; instead, the preactivations are constrained to be G-equivariant functions of the network input in a way that couples weights across all layers. The result is a richer family of G-invariant architectures never seen previously. We derive an efficient implementation of G-DNNs after a reparameterization of weights, as well as necessary and sufficient conditions for an architecture to be "admissible"- i.e., nondegenerate and inequivalent to smaller architectures. We include code that allows a user to build a G-DNN interactively layer-by-layer, with the final architecture guaranteed to be admissible. We show that there are far more admissible G-DNN architectures than those accessible with the "concatenated ReLU" activation function from the literature. Finally, we apply G-DNNs to two example problems--(1) multiplication in --1, 1} (with theoretical guarantees) and (2) 3D object classification--finding that the inclusion of signed perm-reps significantly boosts predictive performance compared to baselines with only ordinary (i.e., unsigned) perm-reps.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Direct Prediction of Phonon Density of States With Euclidean Neural Networks

Abstract Machine learning has demonstrated great power in materials design, discovery, and property prediction. However, despite the success of machine learning in predicting discrete properties, challenges remain for continuous property prediction. The challenge is aggravated in crystalline solids due to crystallographic symmetry considerations and data scarcity. Here, the direct prediction of phonon density‐of‐states (DOS) is demonstrated using only atomic species and positions as input. Euclidean neural networks are applied, which by construction are equivariant to 3D rotations, translations, and inversion and thereby capture full crystal symmetry, and achieve high‐quality prediction using a small training set of examples with over 64 atom types. The predictive model reproduces key features of experimental data and even generalizes to materials with unseen elements, and is naturally suited to efficiently predict alloy systems without additional computational cost. The potential of the network is demonstrated by predicting a broad number of high phononic specific heat capacity materials. The work indicates an efficient approach to explore materials' phonon structure, and can further enable rapid screening for high‐performance thermal storage materials and phonon‐mediated superconductors.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Analyzing the Free States of one Quantum Resource Theory as Resource States of Another

In the context of quantum resource theories (QRTs), free states are defined as those that can be obtained at no cost under a certain restricted set of conditions. However, when taking a free state from one QRT and evaluating it through the optics of another QRT, it might well turn out that the state is now extremely resourceful. Such realization has recently prompted numerous works characterizing states across several QRTs. Here, in this work, we contribute to this body of knowledge by analyzing the resourcefulness in free states for—and across witnesses of—the QRTs of multipartite entanglement, fermionic non-Gaussianity, imaginarity, realness, spin coherence, Clifford non-stabilizerness, $S_n$-equivariance, and non-uniform entanglement. We provide rigorous theoretical results as well as present numerical studies that showcase the rich and complex behavior that arises in this type of cross-examination.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

On the intermediate Jacobian of M5-branes

Abstract We study Euclidean M5-branes wrapping vertical divisors in elliptic Calabi-Yau fourfold compactifications of M/F-theory that admit a Sen limit. We construct these Calabi-Yau fourfolds as elliptic fibrations over coordinate flip O3/O7 orientifolds of toric hypersurface Calabi-Yau threefolds. We devise a method to analyze the Hodge structure (and hence the dimension of the intermediate Jacobian) of vertical divisors in these fourfolds, using only the data available from a type IIB compactification on the O3/O7 Calabi-Yau orientifold. Our method utilizes simple combinatorial formulae (that we prove) for the equivariant Hodge numbers of the Calabi-Yau orientifolds and their prime toric divisors, along with a formula for the Euler characteristic of vertical divisors in the corresponding elliptic Calabi-Yau fourfold. Our formula for the Euler characteristic includes a conjectured correction term that accounts for the contributions of pointlike terminal ℤ 2 singularities corresponding to perturbative O3-planes. We check our conjecture in a number of explicit examples and find perfect agreement with the results of direct computations.

Physics↗
DOE OSTI2023

Non-isometric codes for the black hole interior from fundamental and effective dynamics

We introduce a new holographic map for encoding black hole interiors by including both fundamental and effective dynamics. This holographic map is constructed by evolving a state in the effective, semiclassical gravity description of the interior backwards in time to pull the degrees of freedom outside the black hole, before evolving forwards in time in the fundamental description. We show this “backwards-forwards” map is equivalent to a post-selection map of the type introduced by Akers, Engelhardt, Harlow, Penington, and Vardhan, and in the case of trivial effective interactions reduces to their model, while providing a suitable generalization when those interactions are nontrivial. We show the map is equivariant with respect to time evolution, and independent of any interactions outside the black hole. This construction includes interactions with an infaller in a way that preserves the unitarity of black hole evolution exactly and does not allow for superpolynomial computational complexity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

2D Dilaton Gravity and the Weil–Petersson Volumes with Conical Defects

We derive the Weil-Petersson measure on the moduli space of hyperbolic surfaces with defects of arbitrary opening angles and use this to compute its volume. We conjecture a matrix integral computing the corresponding volumes and confirm agreement in simple cases. Here, we combine this mathematical result with the equivariant localization approach to Jackiw-Teitelboim gravity to justify a proposed exact solution of pure 2d dilaton gravity for a large class of dilaton potentials.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Commuting Line Defects At $q^N$ = 1

Here, we explain the physical origin of a curious property of algebras $\mathcal{A}_{\mathfrak{q}}$ which encode the rotation-equivariant fusion ring of half-BPS line defects in four-dimensional $\mathcal{N}$ = 2 supersymmetric quantum field theories. These algebras are a quantization of the algebras of holomorphic functions on the three-dimensional Coulomb branch of the SQFTs, with deformation parameter log $\mathfrak{q}$. They are known to acquire a large center, canonically isomorphic to the undeformed algebra, whenever $\mathfrak{q}$ is a root of unity. We give a physical explanation of this fact. We also generalize the construction to characterize the action of this center in the $\mathcal{A}_{\mathfrak{q}}$-modules associated to three-dimensional $\mathcal{N}$ = 2 boundary conditions. Finally, we use dualities to relate this construction to a construction in the Kapustin–Witten twist of four-dimensional $\mathcal{N}$ = 4 gauge theory. These considerations give simple physical explanations of certain properties of quantized skein algebras and cluster varieties, and quantum groups, when the deformation parameter is a root of unity.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Data-Driven Operator Theoretic Methods for Phase Space Learning and Analysis

This paper uses data-driven operator theoretic approaches to explore the global phase space of a dynamical system. In this work, we defined conditions for discovering new invariant subspaces in the state space of a dynamical system starting from an invariant subspace based on the spectral properties of the Koopman operator. When the system evolution is known locally in several invariant subspaces in the state space of a dynamical system, a phase space stitching result is derived that yields the global Koopman operator. Additionally, in the case of equivariant systems, a phase space stitching result is developed to identify the global Koopman operator using the symmetry properties between the invariant subspaces of the dynamical system and time-series data from any one of the invariant subspaces. Finally, these results are extended to topologically conjugate dynamical systems; in particular, the relation between the Koopman tuple of topologically conjugate systems is established. The proposed results are demonstrated on several second-order nonlinear dynamical systems including a bistable toggle switch. Our method elucidates a strategy for designing discovery experiments: experiment execution can be done in many steps, and models from different invariant subspaces can be combined to approximate the global Koopman operator.

42 ENGINEERING↗
DOE OSTI2022

Exploiting Machine Learning in Multiscale Modelling of Materials

Recent developments in efficient machine learning algorithms have spurred significant interest in the materials community. The inherently complex and multiscale problems in Materials Science and Engineering pose a formidable challenge. The present scenario of machine learning research in Materials Science has a clear lacunae, where efficient algorithms are being developed as a separate endeavour, while such methods are being applied as ‘black-box’ models by others. The present article aims to discuss pertinent issues related to the development and application of machine learning algorithms for various aspects of multiscale materials modelling. The authors present an overview of machine learning of equivariant properties, machine learning-aided statistical mechanics, the incorporation of ab initio approaches in multiscale models of materials processing and application of machine learning in uncertainty quantification. In addition to the above, the applicability of Bayesian approach for multiscale modelling will be discussed. Critical issues related to the multiscale materials modelling are also discussed.

42 ENGINEERING↗
DOE OSTI2026

Actinium–DOTA coordination in water from hybrid ML/MM: Structure, free energies, and water-exchange pathways

Quantitative simulation of trivalent ƒ-block chelates in water remains challenging because bonded and non-bonded force-field models make different approximations for coordination structure, exchange dynamics, and ion–ligand interactions in highly charged systems. Here, we develop a hybrid machine-learning/molecular-mechanics (ML/MM) framework for Ac 3+ –DOTA in explicit solvent by training an E(3)-equivariant neural network potential (MACELES) on mechanically embedded QM/MM data for Ac aquo and Ac–DOTA species and coupling it to NAMD 2.14 with particle-mesh Ewald electrostatics. Nanosecond ML/MM trajectories remain numerically stable and preserve chelate integrity, yielding a compact DOTA inner shell with an inner-sphere water coordination number of CN Ac,O w ≈ 1.7 arising from a dynamic equilibrium between one- and two-water states (37.5% and 59.9% of frames; three waters 2.5%). A 5 ns potential of mean force shows two low-lying basins at CN Ac,O w ≈ 1 and CN Ac,O w ≈ 2. DFT end-state free energies are consistent with the ML/MM profile, and DFT minimum-energy paths provide a qualitative electronic-structure reference for the observed basin connectivity. State-resolved kinetics reveal picosecond water-exchange pathways that couple hydration changes to transient DOTA arm fluctuations, and training-set comparisons show that temperature-matched Ac–DOTA data optimize energy/force accuracy while more diverse solvated data improve charge prediction. Overall, the present hybrid ML/MM model provides a practical description of Ac 3+ –DOTA hydration thermodynamics and short-time exchange behavior in explicit water at MD-like cost.

Actinium↗
DOE OSTI2025

Generalizable machine learning potentials for quantum-accurate predictions of non-equilibrium behavior in 2D materials

Machine learning interatomic potentials (ML-IAPs) are emerging as transformative tools in materials modeling, promising quantum-level accuracy at a fraction of the computational cost. However, their ability to generalize beyond equilibrium configurations and to reliably capture defect- and temperature-driven behavior remains underexplored. Here, we develop and benchmark two state-of-the-art ML-IAPs, Spectral Neighbor Analysis Potential (SNAP) and Allegro, on a comprehensive dataset for monolayer MoSe₂. Using density functional theory (DFT) as the reference, we evaluate their performance in capturing stress–strain behavior, phase transition energetics, defect evolution, edge stability, and fracture toughness. Allegro, a deep equivariant neural network potential, surpasses both SNAP and the classical Tersoff potential in accuracy, efficiency, and transferability. Importantly, both ML potentials accurately reproduce experimental fracture measurements and ab initio predictions of inversion domain formation—phenomena well beyond their training sets. Our findings establish ML-IAPs as viable replacements for traditional force fields in the study of non-equilibrium mechanical phenomena, enabling large-scale, high-fidelity simulations in 2D materials and beyond. In conclusion, this work provides a broadly applicable framework for data-driven modeling of structural and functional transformations under extreme conditions.

2D materials↗
DOE OSTI2022

Machine learning magnetism classifiers from atomic coordinates

The determination of magnetic structure poses a long-standing challenge in condensed matter physics and materials science. Experimental techniques such as neutron diffraction are resource-limited and require complex structure refinement protocols, while computational approaches such as first-principles density functional theory (DFT) need additional semi-empirical correction, and reliable prediction is still largely limited to collinear magnetism. Here, we present a machine learning model that aims to classify the magnetic structure by inputting atomic coordinates containing transition metal and rare earth elements. By building a Euclidean equivariant neural network that preserves the crystallographic symmetry, the magnetic structure (ferromagnetic, antiferromagnetic, and nonmagnetic) and magnetic propagation vector (zero or non-zero) can be predicted with an average accuracy of 77.8% and 73.6%. In particular, a 91% accuracy is reached when predicting no magnetic ordering even if the structure contains magneticelement(s). Ourworkrepresents onestepforwardtosolvingthegrand challenge of full magnetic structure determination.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Explicitly antisymmetrized neural network layers for variational Monte Carlo simulation

The combination of neural networks and quantum Monte Carlo methods has arisen as a promising path forward for highly accurate electronic structure calculations. Previous proposals have combined equivariant neural network layers with a final antisymmetric layer in order to satisfy the antisymmetry requirements of the electronic wavefunction. However, to date it is unclear if one can represent antisymmetric functions of physical interest, and it is difficult to precisely measure the expressiveness of the antisymmetric layer. Here, this work attempts to address this problem by introducing explicitly antisymmetrized universal neural network layers. This approach has a computational cost which increases factorially with respect to the system size, but we are nonetheless able to apply it to small systems to better understand how the structure of the antisymmetric layer affects its performance. We first introduce a generic antisymmetric (GA) neural network layer, which we use to replace the entire antisymmetric layer of the highly accurate ansatz known as the FermiNet. We demonstrate that the resulting FermiNet-GA architecture can yield effectively the exact ground state energy for small atoms and molecules. We then consider a factorized antisymmetric (FA) layer which more directly generalizes the FermiNet by replacing the products of determinants with products of antisymmetrized neural networks. We find, interestingly, that the resulting FermiNet-FA architecture does not significantly outperform the FermiNet. This strongly suggests that the sum of products of antisymmetries is a key limiting aspect of the FermiNet architecture. To explore this further, we investigate a slight modification of the FermiNet, called the full determinant mode, which replaces each product of determinants with a single combined determinant. We find that the full single-determinant FermiNet closes a large part of the gap between the standard single-determinant FermiNet and FermiNet-GA on small atomic and molecular problems. Surprisingly, on the nitrogen molecule at a dissociating bond length of 4.0 Bohr, the full single-determinant FermiNet can outperform the largest standard FermiNet calculation with 64 determinants.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Anti-symmetric barron functions and their approximation with sums of determinants

A fundamental problem in quantum physics is to encode functions that are completely anti-symmetric under permutations of identical particles. The architecture of neural network models for the electron wave function typically comprises an equivariant component followed by a summation of determinants. The recently introduced Generic Antisymmetric (GA) block is designed to enhance the expressivity of such neural wave functions, and it was found that the 2-layer GA block achieved more accurate energies than the corresponding single-determinant FermiNet architecure, suggesting its promise as a way to improve the expressivity of neural wave functions. In this paper we show how the function expressed by the 2-layer GA block can be decomposed into a sum of determinants. We formalize this result by defining the antisymmetric Barron space as a generalized version of the 2-layer GA block and providing an appromation theorem for this function class. This result can be viewed as a negative result showing that the 2-layer GA block is not more expressive than using multiple determinants.

Abrahamsen, Nilin↗
DOE OSTI2025

SympGNNs: Symplectic Graph Neural Networks for identifying high-dimensional Hamiltonian systems and node classification

Existing neural network models to learn Hamiltonian systems, such as SympNets, although accurate in low-dimensions, struggle to learn the correct dynamics for high-dimensional many-body systems. Herein, we introduce Symplectic Graph Neural Networks (SympGNNs) that can effectively handle system identification in high-dimensional Hamiltonian systems, as well as node classification. SympGNNs combine symplectic maps with permutation equivariance, a property of graph neural networks. Specifically, we propose two variants of SympGNNs: (i) G-SympGNN and (ii) LA-SympGNN, arising from different parameterizations of the kinetic and potential energy. We demonstrate the capabilities of SympGNN on two physical examples: a 40-particle coupled Harmonic oscillator, and a 2000-particle molecular dynamics simulation in a two-dimensional Lennard-Jones potential. Furthermore, we demonstrate the performance of SympGNN in the node classification task, achieving accuracy comparable to the state-of-the-art. Finally, we also empirically show that SympGNN can overcome the oversmoothing and heterophily problems, two key challenges in the field of graph neural networks.

Deep learning↗