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DOE OSTI2025

Learning and discovering multiple solutions using physics-informed neural networks with random initialization and deep ensemble

In this work we explore the capability of physics-informed neural networks (PINNs) to discover multiple solutions. Many real-world phenomena governed by nonlinear differential equations (DEs), such as fluid flow, exhibit multiple solutions under the same conditions, yet capturing this solution multiplicity remains a significant challenge. A key difficulty lies in providing appropriate initial conditions or guesses, as widely used time-marching schemes and Newton’s method are highly sensitive to these choices when solving complex computational problems. While machine learning models, particularly PINNs, have shown promise in solving DEs, their ability to capture multiple solutions remains underexplored. In this work, we propose a simple and practical approach using PINNs to learn and discover multiple solutions. We first demonstrate that PINNs, when combined with random initialization and deep ensemble method—originally developed for uncertainty quantification—can effectively uncover multiple solutions to nonlinear ordinary and partial DEs. Although training large ensembles of PINNs may appear computationally demanding, this can be done efficiently using vectorization techniques supported by modern deep learning frameworks, allowing many networks to be trained simultaneously. Our approach highlights the critical role of initialization in shaping solution diversity, addressing an often-overlooked aspect of machine learning for scientific computing. Furthermore, we propose utilizing PINN-generated solutions as initial conditions or initial guesses for conventional numerical solvers to enhance accuracy and efficiency in capturing multiple solutions. Extensive numerical experiments, including the Allen–Cahn equation and cavity flow, where our approach successfully identifies both stable and unstable solutions, validate the effectiveness of our method. These findings establish a general and efficient framework for addressing solution multiplicity in nonlinear DEs.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

A Scaling Study for Incompressible Multispecies Solver in Vertex-CFD

Multispecies incompressible flows occur widely in engineering and environmental applications, such as chemical reactors, fuel cells, ocean mixing, and biomedical systems. However, accurately resolving the complex transport and mixing phenomena associated with multiple interacting species remains computationally challenging, especially for large-scale problems. In this study, we present a robust, high-performance computing--enabled multispecies incompressible Navier–Stokes solver integrated within the Vertex-CFD framework. Our solver employs a fully coupled, implicit, finite element--based formulation that accurately captures the advection, diffusion, and interaction of multiple species in incompressible flows by leveraging the Kokkos library for parallel computing to achieve high computational efficiency. For pressure coupling, the entropically damped artificial compressibility method is utilized. We validated the solver against canonical test cases, including multispecies advection, diffusion, and Bateman systems; the results demonstrate second- and third-order spatial accuracy and consistent convergence. Additionally, we demonstrated the strong and weak scaling study results obtained on the leadership-class high-performance computing system, Frontier at Oak Ridge National Laboratory.

Oz, Furkan [ORNL] (ORCID:0000000265831724)↗

DOE OSTI2024

SmartFuse: Reconfigurable Smart Switches to Accelerate Fused Collectives in HPC Applications

Communication switches have sometimes been augmented to process collectives (e.g., the IBM BlueGene project and the Mellanox SHArP switch). In this work, we find that there is a great acceleration opportunity through the further augmentation of switches to accelerate more complex functions that combine communication with computation. We consider three types of such functions. The first is fully-fused collectives built by fusing multiple existing collectives like Allreduce with Alltoall. The second is semi-fused collectives built by combining a collective with another computation. The third we refer to as higher-order collectives built by combining multiple computations and communications, such as to perform matrix-matrix multiply (PGEMM). In this work, we propose a framework called SmartFuse to accelerate fused collective functions. The core of SmartFuse is a reconfigurable smart switch to support these operations. The semi/fully fused collectives are implemented with a CGRAlike architecture, while higher-order collectives are implemented with a more specialized computational unit that can also schedule communication. Supporting our framework is software to evaluate and translate relevant parts of the input program, compile them into a control data flow graph, and then map this graph to the switch hardware. The proposed framework, once deployed, has the strong potential to accelerate existing HPC applications transparently by encapsulation within an MPI implementation. Experimental results show that this approach improves the performance of the PGEMM kernel, MINIFE, and AMG by, on average, 94%, 15%, and 13%, respectively.

Haghi, Pouya↗

DOE OSTI2025

Temperature Field Reconstruction of Surfaces Heated Through Radiative Heat Transfer Using Convolutional Neural Networks

Microreactors could play a crucial role in decarbonizing our energy portfolio. However, their development and implementation come with specific challenges, particularly regarding cost. Due to their compact size and the harsh operational environment, collecting real-time data on reactor operation can be challenging. Many probe designs are unable to withstand extreme conditions (e.g., temperature, radiation) in the reactor. In this context, using convolutional neural networks (CNNs) can pave the way for developing a nonintrusive approach that relies solely on ex-core sensors. A well-trained physics-informed CNN can reconstruct the distribution of a given physical quantity over a domain using only a few sensors, allowing us to reconstruct the desired field distribution even in a limited space or complex geometries where a large array of sensors is impractical. In this work, we present the initial steps toward developing a real-time tool for monitoring the thermal behavior of nuclear reactor pressure vessels. Based on an experimental setup, a computational model using the Multiphysics Object-Oriented Simulation Environment (moose) framework was built, where the Ray Tracing and Heat Conduction modules were used to evaluate the temperature distribution over a convex metal surface heated through radiative heat transfer. This metal surface represents a section of a heated nuclear reactor vessel wall. The model also accounts for solid mechanics physics through the moose Solid Mechanics module. In situ experimental data, acquired from a Texas A&M facility, were used to validate the computational model. Part of the data generated by the moose model was used to train the convolutional neural network to reconstruct the vessel wall's outer surface temperature. The CNN generalization was then compared against the experimental and computational data.

Aldeia Machado, Luiz Carlos↗

DOE OSTI2025

Enriched immersed finite element and isogeometric analysis: algorithms and data structures

Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their implementation remains a major challenge due to, among other things, the need to apply nontrivial stabilization schemes and generate custom quadrature rules. This article introduces the robust and computationally efficient algorithms and data structures comprising an immersed finite element preprocessing framework. The input to the preprocessor consists of a background mesh and one or more geometries defined on its domain. The output is structured into groups of elements with custom quadrature rules formatted such that common finite element assembly routines may be used without or with only minimal modifications. The key to the preprocessing framework is the construction of material topology information, concurrently with the generation of a quadrature rule, which is then used to perform enrichment and generate stabilization rules. While the algorithmic framework applies to a wide range of immersed finite element methods using different types of meshes, integration, and stabilization schemes, the preprocessor is presented within the context of the extended isogeometric analysis. This method utilizes a structured B-spline mesh, a generalized Heaviside enrichment strategy considering the material layout within individual basis functions’ supports, and face-oriented ghost stabilization. Using a set of examples, the effectiveness of the enrichment and stabilization strategies is demonstrated alongside the preprocessor’s robustness in geometric edge cases. Additionally, the performance and parallel scalability of the implementation are evaluated.

Computer implementation↗

DOE OSTI2026

Goal-oriented real-time Bayesian inference for linear autonomous dynamical systems with application to digital twins for tsunami early warning

We present a goal-oriented framework for constructing digital twins with the following properties: (1) they employ discretizations of high-fidelity partial differential equation (PDE) models governed by autonomous dynamical systems, leading to large-scale forward problems; (2) they solve a linear inverse problem to assimilate observational data to infer uncertain model components followed by a forward prediction of the evolving dynamics; and (3) the entire end-to-end, data-to-inference-to-prediction computation is carried out without approximation and in real time through a Bayesian framework that rigorously accounts for uncertainties. Several challenges must be overcome to realize this framework, including the large scale of the forward problem, the high dimensionality of the parameter space, and for a class of problems including those we target, the slow decay of the singular values of the parameter-to-observable map. Here we introduce a methodology to overcome these challenges by exploiting the autonomous structure of the forward model to decompose the solution of the inverse problem into a one-time-only offline phase in which the PDE model is solved a limited number of times (equal to the number of sensors), and an online phase that maps well onto GPUs and computes the parameter inference and prediction of quantities of interest in real time, given observational data. Our ultimate goal is to apply this framework to construct digital twins for subduction zones, including Cascadia, to provide early warning for tsunamis generated by megathrust earthquakes. To this end, we demonstrate how our methodology can be used to employ seafloor pressure observations, along with the coupled acoustic–gravity wave equations, to infer the earthquake-induced spatiotemporal seafloor motion (discretized with $\mathscr{O}$ (10 9 ) parameters) and forward predict the tsunami propagation. We present results of an end-to-end inference, prediction, and uncertainty quantification for a representative test problem with $\mathscr{O}$ (10 8 ) inversion parameters for which goal-oriented Bayesian inference is accomplished exactly and in real time, that is, in a matter of seconds.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

A physics-constrained neural ordinary differential equations approach for robust learning of stiff chemical kinetics

The high computational cost associated with solving for detailed chemistry poses a significant challenge for predictive computational fluid dynamics (CFD) simulations of turbulent reacting flows. While deep learning techniques have been explored to develop faster surrogate models, they often fail to integrate reliably with CFD solvers. This instability arises because traditional deep learning approaches optimize for training error without ensuring compatibility with ordinary differential equation (ODE) solvers, resulting in accumulation of errors over time. Recently, neuralODE (NODE) based approaches have been shown to be a promising technique to emulate and accelerate detailed chemistry computations. Here, in the present work, we extend this NODE framework for stiff chemical kinetics by incorporating mass conservation constraints directly into the loss function during training. This ensures that the total mass as well as the individual elemental species masses are conserved in an a-posteriori manner. Proof-of-concept studies are performed with the novel physics-constrained NODE (PC-NODE) approach for homogeneous autoignition of hydrogen-air mixture over a range of composition and thermodynamic conditions. It is demonstrated that the PC-NODE framework not only improves the physical consistency of the resulting data-driven model with respect to mass conservation criteria, but also improves training efficiency. PC-NODE is shown to achieve 2–100× speedup relative to the hydrogen-air detailed chemical mechanism depending on the type of the ODE solver (implicit or explicit) used during autoregressive inference tests. Lastly, a-posteriori studies are performed wherein the trained PC-NODE model is coupled with a CFD solver. It is shown that higher accuracy is achieved with PC-NODE relative to the purely data-driven NODE approach. Moreover, PC-NODE also exhibits robustness and generalizability to unseen initial conditions from within (interpolative capability) as well as outside (extrapolative capability) the training regime.

computational combustion↗

DOE OSTI2024

Effective many-body interactions in reduced-dimensionality spaces through neural network models

Accurately describing properties of challenging problems in physical sciences often requires complex mathematical models that are unmanageable to tackle head on. Therefore, developing reduced-dimensionality representations that encapsulate complex correlation effects in many-body systems is crucial to advance the understanding of these complicated problems. However, a numerical evaluation of these predictive models can still be associated with a significant computational overhead. To address this challenge, in this paper we discuss a combined framework that integrates recent advances in the development of active-space representations of coupled cluster (CC) downfolded Hamiltonians with neural network approaches. The primary objective of this effort is to train neural networks to eliminate the computationally expensive steps required for evaluating hundreds or thousands of Hugenholtz diagrams, which correspond to multidimensional tensor contractions necessary for evaluating a many-body form of downfolded effective Hamiltonians. Using small molecular systems (the H 2 O and HF molecules) as examples, we demonstrate that training neural networks employing effective Hamiltonians for a few nuclear geometries of molecules can accurately interpolate or extrapolate their forms to other geometrical configurations characterized by different intensities of correlation effects. We also discuss differences between effective interactions that define CC downfolded Hamiltonians with those of bare Hamiltonians defined by Coulomb interactions in the active spaces. Published by the American Physical Society 2024

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Accelerated Depth Computation for Surface Boxplots with Deep Learning

Functional depth is a well-known technique used to derive descriptive statistics (e.g., median, quartiles, and outliers) for 1D data. Surface boxplots extend this concept to ensembles of images, helping scientists and users identify representative and outlier images. However, the computational time for surface boxplots increases cubically with the number of ensemble members, making it impractical for integration into visualization tools. In this paper, we propose a deep-learning solution for efficient depth prediction and computation of surface boxplots for time-varying ensemble data. Our deep learning framework accurately predicts member depths in a surface boxplot, achieving average speedups of 6X on a CPU and 15X on a GPU for the 2D Red Sea dataset with 50 ensemble members compared to the traditional depth computation algorithm. Our approach achieves at least a 99% level of rank preservation, with order flipping occurring only at pairs with extremely similar depth values that pose no statistical differences. This local flipping does not significantly impact the overall depth order of the ensemble members.

Han, Mengjiao↗

DOE OSTI2025

A Brief Survey on High Performance Computing Systems Power Management

This paper provides a survey of software-based power management techniques in High Performance Computing (HPC) systems. Seven existing power management and monitoring tools and frameworks are discussed. These are: Variorum, dynamic energy-performance optimizer (DEPO), Powersched, Bull Dynamic Power Optimizer (BDPO), Energy Aware Runtime (EAR), Global Extensible Open Power Manager (GEOPM), and PoLiMEr. Each of these tools is evaluated based on hardware abstraction, optimization methods, usability, and experimental validation. This survey highlights the diversity of approaches in managing energy efficiency, from vendor-neutral APIs to algorithm-driven power capping, and dynamic frequency adjustments. Given that energy requirements for large computational systems is increasing quickly, the importance of integrating these tools into existing HPC environments and the need for further research in this rapidly evolving field is also discussed.

97 - MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Developing Digital Twin Visualizations: A Methodology and Case Study on Chemical Separation Processing

As advances in digital engineering continue to push the technological boundaries, digital twin (DT) visualizations for diagnostics and safeguards advancement become much more feasible and practical. DTs generate large and complex data streams that require effective user interfaces to provide monitoring and diagnostic capabilities. Unfortunately, while these frameworks exist, there is not much research on the systematic documentation of human–computer interaction (HCI) for DT visualization. This work presents a dual-mode visualization methodology (two dimensional [2D] graphical user interface dashboard and 3D mixed reality) designed to support diagnostic tasks in DT systems and building on a validated framework and applying established HCI principles. The methodology is demonstrated through a case study of aqueous processing at Idaho National Laboratory, using experimental data from the chemical solvent extraction runs. Our interfaces display real-time alerts and monitoring to inform users of safeguards anomalies. The interfaces use immersive 3D mixed-reality visualization for further system and experiment investigation. This work demonstrates how the systematic application of HCI principles can inform DT visualization design for diagnostic and safeguards applications. While formal user evaluation studies remain as future work, this paper documents the systematic design methodology and demonstrates a proof-of-concept implementation.

3D visualization↗

DOE OSTI2025

NGEE Arctic Phase 4 Plant Functional Type Framework for Pan-Arctic Vegetation

The NGEE-Arctic research team identified a common set of hierarchical plant functional types (PFTs) for pan-arctic vegetation that we will use across our research activities. Interdisciplinary work within a large team requires agreement regarding levels of functional organization so that knowledge, data, and technologies can be shared and combined effectively. The team has identified plant functional types as a crucial area where such interoperability is needed. PFTs are used to represent plant pools and fluxes within models, summarize observational data, and map vegetation across the landscape. Within each of these applications, varying levels of PFT specificity are needed according to the specific scientific research goal, computational limitations, and data availability. By agreeing on a specific hierarchical framework for grouping variables in our vegetation data, we ensure the resulting research products will be robust, flexible, and scalable. In this document, we lay out the agreed upon PFT framework with definitions and references to existing literature. Table 1 included in the "NGA700_Phase4PFTFramework_about*" file outlines the relationship between NGEE-Arctic Phase 4, Tier 1 PFTs and the PFTs used within prominent arctic literature as well as publications by the NGEE-Arctic team during phases 1-3.This dataset consists of a table detailing a hierarchical PFT framework that spans 4 tiers with the most granular PFTs listed in tier 1 and the most general PFTs in tier 4. The PFTs within each tier has a single column in the dataset where the PFTs are named and a separate column where the characteristics used to define that PFT are listed. Grey fill of the cells is used to indicate where a given PFT starts to “lose” tier 1 details as you look from left to right. Note the excel file has merged cells to indicate grouping of PFTs across the Tiers- it will not translate into a delimited filetype (.csv, .txt, etc) without modification thus the hierarchical PFT framework table is available in three different file formats: 1) NGA700_Phase4PTS.xlsx – maintains the merged cells and grey fill; 2) NGA700_Phase4PTS.csv – merged cells are split, and grey fill is removed; 3) NGA700_Phase4PTS.pdf – image of the table with merged cells and grey fill. Metadata document included as a *.pdf and file-level metadata and data dictionary as *.csv files.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Automated Membership Inference Attacks: Discovering MIA Signal Computations using LLM Agents

Membership inference attacks (MIAs), which enable adversaries to determine whether specific data points were part of a model's training dataset, have emerged as an important framework to understand, assess, and quantify the potential information leakage associated with machine learning systems. Designing effective MIAs is a challenging task that usually requires extensive manual exploration of model behaviors to identify potential vulnerabilities. In this paper, we introduce AutoMIA -- a novel framework that leverages large language model (LLM) agents to automate the design and implementation of new MIA signal computations. By utilizing LLM agents, we can systematically explore a vast space of potential attack strategies, enabling the discovery of novel strategies. Our experiments demonstrate AutoMIA can successfully discover new MIAs that are specifically tailored to user-configured target model and dataset, resulting in improvements of up to 0.18 in absolute AUC over existing MIAs. This work provides the first demonstration that LLM agents can serve as an effective and scalable paradigm for designing and implementing MIAs with SOTA performance, opening up new avenues for future exploration.

Tran, Toan Viet [Emory University]↗

DOE OSTI2026

E-PINNs: Epistemic Physics-Informed Neural Networks

Physics-informed neural networks (PINNs) have demonstrated promise as a framework for solving forward and inverse problems involving partial differential equations. Despite recent progress in the field, it remains challenging to quantify uncertainty in these networks. While techniques such as Bayesian PINNs (B-PINNs) provide a principled approach to capturing epistemic uncertainty through Bayesian inference, they can be computationally expensive for large-scale applications. In this work, we propose Epistemic Physics-Informed Neural Networks (E-PINNs), a framework that uses a small network, the epinet, to efficiently quantify epistemic uncertainty in PINNs. The proposed approach works as an add-on to existing, pre-trained PINNs with a small computational overhead. We demonstrate the applicability of the proposed framework in various test cases and compare the results with B-PINNs using Hamiltonian Monte Carlo (HMC) posterior estimation and dropout-equipped PINNs (Dropout-PINNs). In our experiments, E-PINNs achieve calibrated coverage with competitive sharpness at substantially lower cost. We demonstrate that when B-PINNs produce narrower bands, they under-cover in our tests. E-PINNs also show better calibration than Dropout-PINNs in these examples, indicating a favorable accuracy-efficiency trade-off.

AI for Science↗

DOE OSTI2025

Quantum error mitigation for Fourier moment computation

Hamiltonian moments in Fourier space—expectation values of the unitary evolution operator under a Hamiltonian at different times—provide a convenient framework to understand quantum systems. They offer insights into the energy distribution, higher-order dynamics, response functions, correlation information, and physical properties. This paper focuses on the computation of Fourier moments within the context of a nuclear effective field theory on superconducting quantum hardware. The study integrates echo verification and noise renormalization into Hadamard tests using control reversal gates. These techniques, combined with purification and error suppression methods, effectively address quantum hardware decoherence. The analysis, conducted using noise models, reveals a significant reduction in noise strength by two orders of magnitude. Moreover, quantum circuits involving up to 266 gates over five qubits demonstrate high accuracy under these methodologies when run on IBM superconducting quantum devices. Published by the American Physical Society 2025

Kiss, Oriel (ORCID:0000000174613342)↗

DOE OSTI2026

Combination and interpretation of differential Higgs boson production cross sections in proton-proton collisions at $ \sqrt{s}=13 $ TeV

Precision measurements of Higgs boson differential production cross sections are a key tool to probe the properties of the Higgs boson and test the standard model. New physics can affect both Higgs boson production and decay, leading to deviations from the distributions that are expected in the standard model. In this paper, combined measurements of differential spectra in a fiducial region matching the experimental selections are performed, based on analyses of four Higgs boson decay channels (γγ, ZZ$^{(*)}$, WW$^{(*)}$, and ττ) using proton-proton collision data recorded with the CMS detector at $ \sqrt{s}=13 $ TeV, corresponding to an integrated luminosity of 138 fb$^{−1}$. The differential measurements are extrapolated to the full phase space and combined to provide the differential spectra. A measurement of the total Higgs boson production cross section is also performed using the γγ and ZZ decay channels, with a result of $ {53.4}_{-2.9}^{+2.9}{\left(\textrm{stat}\right)}_{-1.8}^{+1.9}\left(\textrm{syst}\right) $ pb, consistent with the standard model prediction of 55.6 ± 2.5 pb. The fiducial measurements are used to compute limits on Higgs boson couplings using the κ-framework and the SM effective field theory.[graphic not available: see fulltext]

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

FAIR Data and Interpretable AI Framework for Architectured Metamaterials

Our interdisciplinary effort successfully generated FAIR (Findable, Accessible, Interoperable, and Reusable) benchmark datasets for mechanical metamaterials while introducing a novel Artificial Intelligence (AI) framework known as Learning Refined Compositional Rules (LRCR). This framework was specifically designed to bridge the gap across varying computational length scales and extract the underlying physical mechanisms that connect a material's structural geometry to its bulk acoustic properties. Historically, the discovery of such structured materials relied heavily on human intuition or opaque, black-box optimization algorithms that were difficult to generalize. By combining interpretable machine learning techniques with rigorous experimental validation, this project established clear, generalizable design guidelines for tuning wave dispersion and controlling vibrations. Ultimately, the public availability of these structured datasets and algorithms will significantly reduce computational costs and accelerate the design of advanced multi-functional acoustic devices, offering broad societal impacts across fields like aerospace engineering, telecommunications, and biomedical implant design.

36 MATERIALS SCIENCE↗

DOE OSTI2025

SineKAN: Kolmogorov-Arnold Networks using sinusoidal activation functions

Recent work has established an alternative to traditional multi-layer perceptron neural networks in the form of Kolmogorov-Arnold Networks (KAN). The general KAN framework uses learnable activation functions on the edges of the computational graph followed by summation on nodes. The learnable edge activation functions in the original implementation are basis spline functions (B-Spline). Here, we present a model in which learnable grids of B-Spline activation functions are replaced by grids of re-weighted sine functions (SineKAN). We evaluate numerical performance of our model on a benchmark vision task. We show that our model can perform better than or comparable to B-Spline KAN models and an alternative KAN implementation based on periodic cosine and sine functions representing a Fourier Series. Further, we show that SineKAN has numerical accuracy that could scale comparably to dense neural networks (DNNs). Compared to the two baseline KAN models, SineKAN achieves a substantial speed increase at all hidden layer sizes, batch sizes, and depths. Current advantage of DNNs due to hardware and software optimizations are discussed along with theoretical scaling. Additionally, properties of SineKAN compared to other KAN implementations and current limitations are also discussed.

Reinhardt, Eric↗