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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
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DOE OSTI2025

On the Recoverability of Reactor Dynamics from Point Kinetics Data using SINDYc

Data driven models for reactor dynamics tend to face a few notable challenges. First, the broad range of timescales present across the various feedback mechanisms. Next, high standards for safety and importance of model performance in all operational domains. Finally, the correlations between state variables observed in most transients leads to difficulties when methods attempt to attribute certain dynamic phenomena to a particular cause. The current paper seeks to support efforts towards incorporating physics knowledge into one particular data-driven method for finding reactor dynamics called ``Sparse Identification of Nonlinear Dynamics with Control (SINDYc). The incorporation of physical knowledge into SINDYc will help address the challenges listed above by giving the model an initial understanding of the system being modeled. The demonstration of an exact representation of a set of point reactor dynamics equations in SINDYc is provided. Then, this allows for further discussion with mathematical justification as to why SINDYc, and other data-driven methods, may be difficult to apply to nuclear reactor dynamics due to correlations in the state variables. A particularly useful result of this work is the set of candidate functions required in SINDYc to exactly represent the reactor dynamics under a point approximation. In the future, SINDYc can be integrated with point models for reactor dynamics before being applied to the physical system to yield higher accuracy.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Tree tensor network hierarchical equations of motion based on time-dependent variational principle for efficient open quantum dynamics in structured thermal environments

In this work, we introduce an efficient method, TTN-HEOM, for exactly calculating the open quantum dynamics for driven quantum systems interacting with highly structured bosonic baths by combining the tree tensor network (TTN) decomposition scheme with the bexcitonic generalization of the numerically exact hierarchical equations of motion (HEOM). The method yields a series of quantum master equations for all core tensors in the TTN that efficiently and accurately capture the open quantum dynamics for non-Markovian environments to all orders in the system–bath interaction. These master equations are constructed based on the time-dependent Dirac–Frenkel variational principle, which isolates the optimal dynamics for the core tensors given the TTN ansatz. The dynamics converges to the HEOM when increasing the rank of the core tensors, a limit in which the TTN ansatz becomes exact. We introduce TENSO, tensor equations for non-Markovian structured open systems, as a general-purpose Python code to propagate the TTN-HEOM dynamics. We implement three general propagators for the coupled master equations: two fixed-rank methods that require a constant memory footprint during the dynamics and one adaptive-rank method with a variable memory footprint controlled by the target level of computational error. We exemplify the utility of these methods by simulating a two-level system coupled to a structured bath containing one Drude–Lorentz component and eight Brownian oscillators, which is beyond what can presently be computed using the standard HEOM. Our results show that the TTN-HEOM is capable of simulating both dephasing and relaxation dynamics of driven quantum systems interacting with structured baths, even those of chemical complexity, with an affordable computational cost.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Shadow molecular dynamics for flexible multipole models

Shadow molecular dynamics provide an efficient and stable atomistic simulation framework for flexible charge models with long-range electrostatic interactions. Shadow molecular dynamics simulations are driven by approximate “shadow” Born–Oppenheimer potentials for which the exact charges and forces are directly accessible without relying on costly (and approximate) iterative solvers. While previous implementations have been limited to atomic monopole charge distributions, we extend this approach to flexible multipole models. We derive detailed expressions for the shadow energy functions, potentials, and force terms, explicitly incorporating monopole–monopole, dipole–monopole, and dipole–dipole interactions. In our formulation, both atomic monopoles and atomic dipoles are treated as extended dynamical variables alongside the propagation of the nuclear degrees of freedom. We demonstrate that introducing the additional dipole degrees of freedom preserves the stability and accuracy previously seen in monopole-only shadow molecular dynamics simulations. In addition, we present a shadow molecular dynamics scheme where the monopole charges are held fixed while the dipoles remain flexible. Our extended shadow dynamics provide a framework for stable, computationally efficient, and versatile molecular dynamics simulations involving long-range interactions between flexible multipoles. This is of particular current interest in combination with machine-learned interatomic potentials, including long-range electrostatic interactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Probing the Self-Assembly dynamics of cellulose nanocrystals by X-ray photon correlation spectroscopy

Charge-stabilized colloidal cellulose nanocrystals (CNCs) can self-assemble into higher-ordered chiral nematic structures by varying the volume fraction. The assembly process exhibits distinct dynamics during the isotropic to liquid crystal phase transition, which can be elucidated using X-ray photon correlation spectroscopy (XPCS). Anionic CNCs were dispersed in propylene glycol (PG) and water spanning a range of volume fractions, encompassing several phase transitions. Coupled with traditional characterization techniques, XPCS was conducted to monitor the dynamic evolution of the different phases. Additionally, simulated XPCS results were obtained using colloidal rods and compared with the experimental data, offering additional insights into the dynamic behavior of the system. The results indicate that the particle dynamics of CNCs undergo a stepped decay in three stages during the self-assembly process in PG, coinciding with the observed phases. The phase transitions are associated with a total drop of Brownian diffusion rates by four orders of magnitude, a decrease of more than a thousand times slower than expected in an ideal system of repulsive Brownian rods. Given the similarity in the phase behaviors in CNCs dispersed in PG and in water, we hypothesize that these dynamic behaviors can be extrapolated to other polar solvent environments. Importantly, these findings represent the direct measurement of CNC dynamics using XPCS, underscoring the feasibility of directly assessing the dynamic behavior of other rod-like colloidal suspensions.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Backbone Dynamics of Bottlebrush Polymers Studied by Neutron Scattering

Bottlebrush polymers have a versatile architecture that is highly customizable due to the combination of a linear backbone and side chains. As a result of the chemical tethering of the side chains, both parts cannot be easily be separated. Huge effort is seen regarding the dynamical behavior of the side chains or the entire bottlebrush polymer, whereas few studies are available considering the backbone. Here, isotopic labeling in combination with quasi-elastic neutron scattering was used to compare the dynamical behavior of the bottlebrush’s backbone with the side chain dynamics. Keeping the side chains deuterated, (h-PNB)- g -(d-PPO), leads to the scattering signal dominated by backbone dynamics, while the fully protonated sample, (h-PNB)- g -(h-PPO), gives side chain dynamics. Both results reveal slower dynamics associated with the backbone with less heterogeneity, as seen for the side chains. Additionally, a plasticizer effect for the backbone dynamics is confirmed by extracting the glass transition temperature and comparing it with pure linear PNB.

neutron scattering↗
DOE OSTI2026

Local Chain Dynamics in Sequence-Controlled Polymers as a Tunable Handle for Rare Earth Sequestration

Chain dynamics govern the intricate behaviors of proteins, underpinning functions such as catalysis, recognition, and stimulus response, and are an increasingly appreciated aspect of structure–function relationships. Analogously, manipulating chain dynamics and structure in abiotic polymers via sequence control is an exciting, yet underexplored, strategy for improving material functions. In this work, we report a systematic study relating the sequence of polymeric sequestrants to their structure and dynamics, as well as to their binding affinity and selectivity for model substrates, rare earth elements (REEs). A series of sequence-controlled polymers with metal chelating, solubilizing, and structure forming monomers was synthesized via multiblock polymerization, yielding compositionally identical polymers with spectroscopically resolved domains and distinct morphologies. Using a combination of small-angle X-ray scattering and 19 F NMR relaxometry measurements, we connected differences in polymer structure and dynamics to polymer sequence variables such as the patchiness (density) of the structure forming monomer and the location of the chelating monomer. Furthermore, we found that, relative to calcium, all polymers in the series collapse more and have slower dynamics when binding REEs (lanthanum and lutetium) , though the extent of these effects were sequence-dependent and localized to specific domains within the polymer. Notably, sequence-controlled polymers that exhibited the largest conformational and dynamic changes upon binding REEs also bound REEs with the greatest affinity and modest selectivity. Collectively, these results correlate monomer patterning with dynamics, morphology, and REE binding performance en route to the development of efficient and selective macromolecular chelators.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Evaluating crown scorch predictions from a computational fluid dynamics wildland fire simulator

Abstract Background Crown scorch—the heating of live leaves, needles, and buds in the vegetative canopy to lethal temperatures without widespread combustion—is one of the most common fire effects shaping post-fire canopies. Despite the ability of computational fluid dynamic models to finely resolve fire activity and buoyant plume dynamics including heterogenous 3D distributions of forest canopy heating, these models have had only limited use in simulating fire effects and have not been used to evaluate crown scorch. Here, we demonstrate a method of evaluating crown scorch using a computational fluid dynamics model, FIRETEC, and validate this approach by simulating the experiments that were used to develop Van Wagner’s 1973 crown scorch model. Results The average scorch height prediction from FIRETEC compares well with the empirical model derived by Van Wagner, which is the most widely used empirical model for crown scorch. We further find that the 3D buoyant plume dynamics from a steady and homogeneous idealized heat source on the ground results in a spatially heterogenous crown scorch pattern reflecting complex heating dynamics that are best represented by percent scorch rather than height of scorch. Conclusions The ability of the computational fluid dynamics model to capture variation in crown scorch due to 3D buoyant plume dynamics provides direct links between forest structure, fire behavior, and fire effects that can be used by forest managers and researchers to better understand how fires result in crown damage under various environmental and management scenarios.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

DyG-DPCD: A Distributed Parallel Community Detection Algorithm for Large-Scale Dynamic Graphs

Dynamic (Temporal) graphs capture the valuable evolution of real-world systems, from the continuously evolving patterns of social interactions and genetic pathways to the dynamic fluctuations of economic forces. Detecting communities for such evolving networks poses unique challenges. Detecting and analyzing the evolution of communities within dynamic graphs unlocks valuable insights into the underlying structural and temporal patterns of real-world systems. However, the sheer volume of modern graph data and the inherent complexity of the temporal dimension pose significant challenges to scalable community detection algorithms. Addressing this gap, our work explores the limited landscape of scalable distributed-memory parallel methods specifically designed for dynamic network community detection. We propose a novel parallel algorithm, DyG-DPCD (Dynamic Graph Distributed Parallel Community Detection), to detect communities in dynamic networks using the Message Passing Interface (MPI) framework. We present a vertex-centric approach, allowing us to detect communities through local optimization. Furthermore, we enhance our baseline algorithm by incorporating three heuristics, which improve the algorithm’s performance significantly while maintaining the quality of the solutions. We demonstrate the efficiency of our algorithm by experimenting on several real-world large-scale networks with hundreds of millions of edges spanning diverse domains. Notably, DyG-DPCD achieves speedups between 25× and 30× for large networks that we experimented on using NERSC compute nodes. In conclusion, our algorithm outperforms the STINGER parallel re-agglomeration algorithm by 30×.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

An Internal Digital Image Correlation Technique for High-Strain Rate Dynamic Experiments

Full-field, quantitative visualization techniques, such as digital image correlation (DIC), have unlocked vast opportunities for experimental mechanics. However, DIC has traditionally been a surface measurement technique, and has not been extended to perform measurements on the interior of specimens for dynamic, full-scale laboratory experiments. This limitation restricts the scope of physics which can be investigated through DIC measurements, especially in the context of heterogeneous materials. The focus of this study is to develop a method for performing internal DIC measurements in dynamic experiments. The aim is to demonstrate its feasibility and accuracy across a range of stresses (up to 650 MPa), strain rates (10 3 - 10 6 s -1 ), and high-strain rate loading conditions (e.g., ramped and shock wave loading). Internal DIC is developed based on the concept of applying a speckle pattern at an inner-plane of a transparent specimen. The high-speed imaging configuration is coupled to the traditional dynamic experimental setups, and is focused on the internal speckle pattern. During the experiment, while the sample deforms dynamically, in-plane, two-dimensional deformations are measured via correlation of the internal speckle pattern. In this study, the viability and accuracy of the internal DIC technique is demonstrated for split-Hopkinson (Kolsky) pressure bar (SHPB) and plate impact experiments. The internal DIC experimental technique is successfully demonstrated in both the SHPB and plate impact experiments. In the SHPB setting, the accuracy of the technique is excellent throughout the deformation regime, with measurement noise of approximately 0.2% strain. In the case of plate impact experiments, the technique performs well, with error and measurement noise of 1% strain. The internal DIC technique has been developed and demonstrated to work well for full-scale dynamic high-strain rate and shock laboratory experiments, and the accuracy is quantified. Here, the technique can aid in investigating the physics and mechanics of the dynamic behavior of materials, including local deformation fields around dynamically loaded material heterogeneities.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Weighted Composition Operators for Learning Nonlinear Dynamics

Operator theoretic methods in dynamical system have been dominated by the use of Koopman operators and their continuous time counterparts, such as Koopman Generators and Liouville Operators. The advantage gained from their use primarily stems from the ability to extract subspaces and eigenfunctions within a space of observables that are invariant with respect to the Koopman operator over that space. When this occurs, a dynamic mode decomposition of the systems state provides a linear model for the dynamical system. Not all Koopman operators have eigenfunctions that may be exploited in this manner. However, the framework can still be leveraged for approximations using other operators. In this setting, we present a different operator for the study of dynamical systems, the weighted composition operator. These operators are compact for a wide range of dynamics and spaces, and through their interactions with occupation kernels and vector valued kernels, they admit an estimation of the underlying dynamics. Here, this manuscript presents a new algorithm for the data driven study of dynamical systems from data, and also provides two numerical experiments where convergence is achieved as a proof of concept.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Deformation and Delamination of Dynamically Bulging Bilayered Films

We employ finite element simulations to study the dynamic bulging of films under shock tube conditions and compare these responses with quasi-static bulging. Both scenarios subject the film to time-varying pressure. Two film types are considered: uniform material films and bilayers with a relatively soft interior layer and a hard exterior layer. The interface between the materials in the bilayer cases is modeled as a cohesive zone that follows a bilinear normal traction-separation cohesive law. Additionally, bilayer films with preexisting cracks in the interior layer are analyzed. Parametric studies are also conducted to explore the effects of loading rate and specimen size. The mechanical response of all materials is assumed to be strain-rate independent, focusing solely on the inertial effects in the response of the films under dynamic loading, and the absence of such effects under quasi-static loading. The results indicate that quasi-static bulging exhibits a predictable plate bending like deformation. In contrast, depending on the loading rate and specimen size, dynamic bulging can give rise to elastic waves, and a sequence of deformation processes including initial uniform acceleration, followed by bending-like deformation, and finally through-thickness biaxial stretching. Dynamic loading also leads to larger bulge formation and greater deformation than quasi-static loading. A key finding is the role of preexisting cracks in driving delamination under dynamic loading, which is absent in quasi-static loading. This work enhances our understanding of dynamic bulging and motivates further research on characterizing delamination in layered films using dynamic bulge tests.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Real-Space Local Dynamics in 1,2,3-Triazole Using Inelastic Neutron Scattering

Enhancing proton transport in polymer electrolytes is crucial for advancing next-generation solid-state batteries, yet our understanding of proton conductivity in nonaqueous environments remains limited due to a lack of atomic-scale insights. Here, in this study, we investigated the atomic-scale dynamics of 1,2,3-triazole, a small molecule capable of dynamic hydrogen bonding, as a model system for proton hopping in nonaqueous environments. Using the real-space correlation function determined by the double Fourier transformation of inelastic neutron scattering spectra, we identified that the self-motion of protons and intermolecular dynamics occur on comparable time scales. Furthermore, we observed that the activation energy associated with the intermolecular dynamics matches the energy barrier for molecular rotations determined through Density Functional Theory calculations. These findings underscore the importance of controlling molecular dynamics at the atomic scale to control proton transport. Additionally, we demonstrated that intermolecular dynamics in systems involving protons can be studied using inelastic neutron scattering even without deuteration, thereby providing a broader avenue for studying atomic-scale dynamics in soft matter systems.

Shinohara, Yuya [Oak Ridge National Laboratory (OR↗
DOE OSTI2026

Charge Dependence of Local Hydration Dynamics in Poly(Acrylic Acid) Solutions

Localized measurements of hydration dynamics surrounding poly(acrylic acid) (pAA) chains are executed using Overhauser dynamic nuclear polarization relaxometry to determine the role of polymer protonation state on the polymer solvation environment. Alterations in polymer concentration and solution pH uncovered three different regimes of local water dynamics ranging from bulk-water-like to subdued water diffusivity. These experiments, combined with molecular dynamics simulations, reveal that the presence of deprotonated carboxylic acid groups promotes a hydrophilic local environment and extended polymer chain configurations that together incentivize the incorporation of bulk-like water near the polymer. This results in a stretched polymer conformation that leads to faster observed hydration dynamics in the local hydration environment. Meanwhile, protonated carboxylic acid groups are expected to engage in intrapolymer hydrogen bonding between monomer groups, resulting in a more collapsed conformation and slower observed hydration dynamics. The importance of the carboxylic acid groups on mediating hydration behavior is further illustrated by their role in dictating the solvation environment around poly(acrylic acid-stat-(poly(ethylene glycol) methyl ether acrylate) (p(AA-stat-PEGMEA)) copolymers with varying monomer ratios. Furthermore, these local hydration measurements establish a connection between local water dynamics and polymer chain conformation and may provide additional molecular perspective into poly(acrylic acid)’s classification as a superabsorbent polymer.

Conformation↗
DOE OSTI2024

Data-driven discovery of dynamics from time-resolved coherent scattering

Coherent X-ray scattering (CXS) techniques are capable of interrogating dynamics of nano- to mesoscale materials systems at time scales spanning several orders of magnitude. However, obtaining accurate theoretical descriptions of complex dynamics is often limited by one or more factors—the ability to visualize dynamics in real space, computational cost of high-fidelity simulations, and effectiveness of approximate or phenomenological models. In this work, we develop a data-driven framework to uncover mechanistic models of dynamics directly from time-resolved CXS measurements without solving the phase reconstruction problem for the entire time series of diffraction patterns. Our approach uses neural differential equations to parameterize unknown real-space dynamics and implements a computational scattering forward model to relate real-space predictions to reciprocal-space observations. This method is shown to recover the dynamics of several computational model systems under various simulated conditions of measurement resolution and noise. Moreover, the trained model enables estimation of long-term dynamics well beyond the maximum observation time, which can be used to inform and refine experimental parameters in practice. Finally, we demonstrate an experimental proof-of-concept by applying our framework to recover the probe trajectory from a ptychographic scan. Our proposed framework bridges the wide existing gap between approximate models and complex data.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Data-driven Mori–Zwanzig modeling of Lagrangian particle dynamics in turbulent flows

The dynamics of Lagrangian particles in turbulence play a crucial role in mixing, transport, and dispersion in complex flows. Their trajectories exhibit highly nontrivial statistical behavior, motivating the development of surrogate models that can reproduce these trajectories without incurring the high computational cost of direct numerical simulations of the full Eulerian field. This task is particularly challenging because reduced-order models typically lack access to the full set of interactions with the underlying turbulent field. Novel data-driven machine learning techniques can be powerful in capturing and reproducing complex statistics of the reduced-order/surrogate dynamics. In this work, we show how one can learn a surrogate dynamical system that is able to evolve a turbulent Lagrangian trajectory in a way that is point-wise accurate for short-time predictions (with respect to Kolmogorov time) and stable and statistically accurate at long times. This approach is based on the Mori–Zwanzig formalism, which prescribes a mathematical decomposition of the full dynamical system into resolved dynamics that depend on the current state and the past history of a reduced set of observables, and the unresolved orthogonal dynamics due to unresolved degrees of freedom of the initial state. We show how by training this reduced order model on a point-wise error metric on short time-prediction, we are able to correctly learn the dynamics of Lagrangian turbulence, such that also the long-time statistical behavior is stably recovered at test time. This opens up a range of applications, for example, for the control of active Lagrangian agents in turbulence.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Real-space atomic dynamics in liquid gallium studied by inelastic neutron scattering

Gallium is a prototypical liquid metal and has gained renewed attention because of its unique properties. Characterizing and elucidating its atomic dynamics remains elusive despite numerous studies, primarily because of the challenges in quantifying atomic-scale dynamics in liquids. Recent developments in inelastic neutron scattering enable us to measure the Van Hove correlation function that describes the real-space motion of liquid atoms. Here, in this work, we use this approach to reveal the dynamics in gallium liquids and find the co-existence of two dynamical medium-range orders (MROs), which have a dynamical behavior distinct from that of the short-range order (SRO). We propose that these MROs are driven by global forces in the form of two density waves, as a direct consequence of the underlying competition between ionic core repulsion and valence electron cohesion. We suggest that the density wave approach is not only applicable to other metallic liquids exhibiting similar structural anomalies, but also offers a promising direction for elucidating the dynamics of complex liquids and glasses by linking electronic-state fluctuations to atomic dynamics.

Hua, Chengyun [Oak Ridge National Laboratory (ORNL↗
DOE OSTI2024

Dynamic entity formed by protein and its hydration water

The interaction between protein and water plays a pivotal role in shaping the structure, dynamics, and function of biomacromolecules. A comprehensive understanding of this intricate interplay necessitates a systematic evaluation of interaction strength and its consequential impact on the dynamics of proteins and water across diverse protein systems. Despite numerous works on understanding the dynamics of water and proteins and the coupling between them, there are still unanswered questions. Here, we combine neutron scattering and isotope labeling to probe the dynamics of proteins and their hydration water in a variety of protein systems. We consider proteins of different structures and varying thermostability as well as proteins within living cells with distinct growth temperatures. Simultaneous characterization of protein and hydration water dynamics across diverse systems was achieved. Moreover, we performed water sorption isothermal measurements on three representative proteins to correlate the observed dynamics with the strength of the interaction energies governing each system. The experimental results underscore that proteins manifesting stronger attractive interactions with water display diffusionlike dynamics with higher flexibility upon hydration, concomitant with a reduced mobility in hydration water. Significantly, our findings suggest that, in fact, it is the interaction between protein and its hydration water that facilitates the transfer of mobility from water to protein, with stronger interactions correlating to greater protein flexibility and slower hydration water diffusion. Published by the American Physical Society 2024

Ye, Yongfeng (ORCID:0009000792374198)↗
DOE OSTI2025

DS-TIDE: Harnessing Dynamical Systems for Efficient Time-Independent Differential Equation Solving

Time-Independent Differential Equations (TIDEs) are central to modeling equilibrium behavior across a wide range of scientific and engineering domains, from electrostatics to porous media flow. Conventional numerical solvers offer reliable solutions but incur significant computational costs due to fine-grained discretization and iterative procedures. Machine learning-based approaches address this by replacing iterative solving processes with one-time inference; however, their sophisticated models require extensive training resources that often exceed those of traditional solvers. Consequently, designing a TIDE solver that achieves high accuracy, broad applicability, and exceptional computational efficiency remains a fundamental challenge. In this paper, we propose DS-TIDE, a novel hardware solver that is inspired by, and subsequently leverages, the intrinsic connection between Dynamical Systems (DS) and Differential Equations (DEs) to efficiently and accurately solve TIDEs. DS-TIDE employs a CMOS-compatible DS-based processor, whose physical states evolve under carefully designed DE-driven dynamics and naturally converge to equilibrium -- the solution of the target TIDE -- within ~1µs on a ~1-watt DS-TIDE processor. To enhance expressivity, DS-TIDE incorporates Heterogeneous Dynamics with Temporal Layering (HDTL), which solves TIDEs through a three-stage DS evolution -- conditioning, solving, and decoding -- each governed by specialized dynamics. The entire evolution process is analogous to an infinitely deep neural network temporally unrolled, offering the system the capability of representing complex equations. Furthermore, DS-TIDE is equipped with an on-device DS-DE Auto-Alignment mechanism that dynamically adapts intrinsic hardware dynamics within milliseconds, effectively aligning the system’s dynamics to diverse target DEs. Experimental results across TIDEs from a wide range of scientific and engineering domains demonstrate that DS-TIDE achieves ~10^3× speedup, ~10^5× energy savings, and competitive or superior accuracy compared to state-of-the-art numerical and ML-based solvers.

Liu, Chuan↗