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Results for “high-dimensional optimization”

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DOE OSTI2025

Equation-Free Coarse Control of Distributed Parameter Systems via Local Neural Operators

The control of high-dimensional distributed parameter systems (DPS) remains a challenge when explicit coarse-grained equations are unavailable. Classical equation-free (EF) approaches rely on fine-scale simulators treated as black-box timesteppers. However, repeated simulations for steady-state computation, linearization, and control design are often computationally prohibitive, or the microscopic timestepper may not even be available, leaving us with data as the only resource. We propose a data-driven alternative that uses local neural operators, trained on spatiotemporal microscopic/mesoscopic data, to obtain efficient short-time solution operators. These surrogates are employed within Krylov subspace methods to compute coarse steady and unsteady-states, while also providing Jacobian information in a matrix-free manner. Krylov-Arnoldi iterations then approximate the dominant eigenspectrum, yielding reduced models that capture the open-loop slow dynamics without explicit Jacobian assembly. Both discrete-time Linear Quadratic Regulator (dLQR) and pole-placement (PP) controllers are based on this reduced system and lifted back to the full nonlinear dynamics, thereby closing the feedback loop.

93B52, 93C20, 47N70, 65J15, 65M32, 68T07, 68T20, 6↗

DOE OSTI2024

Bayesian Conavigation: Dynamic Designing of the Material Digital Twins via Active Learning

Scientific advancement is universally based on the dynamic interplay between theoretical insights, modeling, and experimental discoveries. However, this feedback loop is often slow, including delayed community interactions and the gradual integration of experimental data into theoretical frameworks. This challenge is particularly exacerbated in domains dealing with high-dimensional object spaces, such as molecules and complex microstructures. Hence, the integration of theory within automated and autonomous experimental setups, or theory in the loop-automated experiment, is emerging as a crucial objective for accelerating scientific research. The critical aspect is to use not only theory but also on-the-fly theory updates during the experiment. Furthermore, we introduce a method for integrating theory into the loop through Bayesian conavigation of theoretical model space and experimentation. Our approach leverages the concurrent development of surrogate models for both simulation and experimental domains at the rates determined by latencies and costs of experiments and computation, alongside the adjustment of control parameters within theoretical models to minimize epistemic uncertainty over the experimental object spaces. This methodology facilitates the creation of digital twins of material structures, encompassing both the surrogate model of behavior that includes the correlative part and the theoretical model itself. While being demonstrated here within the context of functional responses in ferroelectric materials, our approach holds promise for broader applications, such as the exploration of optical properties in nanoclusters, microstructure-dependent properties in complex materials, and properties of molecular systems.

Microscopy↗

DOE OSTI2025

Hyperplane decision trees as piecewise linear surrogate models for chemical process design

Recent trends in chemical engineering research point towards an increasing reliance on data-driven modeling approaches. Neural networks, for instance, have proven to be accurate when data is plentiful and high-dimensional, but in many cases, they require computationally-intensive training procedures. Here, in this work, we describe hyperplane decision trees (HT) as a highly expressive and low-compute machine learning model architecture. These models are locally linear and have linear decision boundaries, resulting in a piecewise linear model of the data. This property allows them to be converted into mixed-integer linear constraints which can be globally optimized. Our open-source PyTorch implementation of this method is a fast, flexible, and accessible way to build accurate piecewise linear models of data.

Decision trees↗

DOE OSTI2024

CO 2 storage site characterization using ensemble-based approaches with deep generative models

Estimating spatially distributed properties such as permeability from available sparse measurements is a great challenge in efficient subsurface CO 2 storage operations. In this paper, a deep generative model that can accurately capture complex subsurface structure is tested with an ensemble-based inversion method for accurate and accelerated characterization of CO 2 storage sites. We chose Wasserstein Generative Adversarial Network with Gradient Penalty (WGAN-GP) for its realistic reservoir property representation and Ensemble Smoother with Multiple Data Assimilation (ES-MDA) for its robust data fitting and uncertainty quantification capability. WGAN-GP are trained to generate high-dimensional permeability fields from a low-dimensional latent space and ES-MDA then updates the latent variables by assimilating available measurements. Several subsurface site characterization examples including Gaussian, channelized, and fractured reservoirs are used to evaluate the accuracy and computational efficiency of the proposed method and the main features of the unknown permeability fields are characterized accurately with reliable uncertainty quantification. Furthermore, the estimation performance is compared with a widely-used variational, i.e., optimization-based, inversion approach, and the proposed approach outperforms the variational inversion method in several benchmark cases. We explain such superior performance by visualizing the objective function in the latent space: because of nonlinear and aggressive dimension reduction via generative modeling, the objective function surface becomes extremely complex while the ensemble approximation can smooth out the multi-modal surface during the minimization. This suggests that the ensemble-based approach works well over the variational approach when combined with deep generative models at the cost of forward model runs unless convergence-ensuring modifications are implemented in the variational inversion.

42 ENGINEERING↗

DOE OSTI2025

An implementation of neural simulation-based inference for parameter estimation in ATLAS

Neural simulation-based inference (NSBI) is a powerful class of machine-learning-based methods for statistical inference that naturally handles high-dimensional parameter estimation without the need to bin data into low-dimensional summary histograms. Such methods are promising for a range of measurements, including at the Large Hadron Collider, where no single observable may be optimal to scan over the entire theoretical phase space under consideration, or where binning data into histograms could result in a loss of sensitivity. This work develops a NSBI framework for statistical inference, using neural networks to estimate probability density ratios, which enables the application to a full-scale analysis. It incorporates a large number of systematic uncertainties, quantifies the uncertainty due to the finite number of events in training samples, develops a method to construct confidence intervals, and demonstrates a series of intermediate diagnostic checks that can be performed to validate the robustness of the method. As an example, the power and feasibility of the method are assessed on simulated data for a simplified version of an off-shell Higgs boson couplings measurement in the four-lepton final states. This approach represents an extension to the standard statistical methodology used by the experiments at the Large Hadron Collider, and can benefit many physics analyses.

frequentist statistics↗

DOE OSTI2025

Efficient calculation of self magnetic field, self-force, and self-inductance for electromagnetic coils with rectangular cross-section

Abstract For designing high-field electromagnets, the Lorentz force on coils needs to be computed in order to design suitable support structures, and the inductance should be computed to evaluate the stored energy and dynamics. Also, the magnetic field and its variation inside the conductor is of interest for computing stress and strain, and due to superconducting quench limits. For these force, inductance, energy, and internal field calculations, the coils cannot be naively approximated as infinitesimally thin filaments due to divergences when the source and evaluation points coincide, so more computationally demanding calculations are usually required, resolving the finite cross-section of the conductors. Here, we present a new alternative method that enables the internal magnetic field vector, self-force, and self-inductance to be computed rapidly and accurately within a 1D filament model. The method is applicable to coils for which the curve center-line can have general noncircular shape, as long as the conductor width is small compared to the radius of curvature. This paper extends a previous calculation for circular-cross-section conductors (Hurwitz et al 2024 IEEE Trans. Magn. ) to consider the case of rectangular cross-section. The reduced model is derived by rigorous analysis of the singularity, regularizing the filament integrals such that they match the true high-dimensional integrals at high coil aspect ratio. The new filament model exactly recovers analytic results for a circular coil, and is shown to accurately reproduce full finite-cross-section calculations for a non-planar coil of a stellarator magnetic fusion device. Due to the efficiency of the model here, it is well suited for use inside design optimization.

Landreman, Matt (ORCID:000000027233577X)↗

DOE OSTI2024

High-dimensional maximum-entropy phase space tomography using normalizing flows

Particle accelerators generate charged-particle beams with tailored distributions in six-dimensional position-momentum space (phase space). Knowledge of the phase space distribution enables model-based beam optimization and control. In the absence of direct measurements, the distribution must be tomographically reconstructed from its projections. In this paper, we highlight that such problems can be severely underdetermined and that entropy maximization is the most conservative solution strategy. We leverage —invertible generative models—to extend maximum-entropy tomography to six-dimensional phase space and perform numerical experiments to validate the model's performance. Our numerical experiments demonstrate consistency with exact two-dimensional maximum-entropy solutions and the ability to fit complicated six-dimensional distributions to large measurement sets in reasonable time. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

Surrogate-Based Autotuning for Randomized Sketching Algorithms in Regression Problems

Algorithms from Randomized Numerical Linear Algebra (RandNLA) are known to be effective in handling high-dimensional computational problems, providing high-quality empirical performance as well as strong probabilistic guarantees. However, their practical application is complicated by the fact that the user needs to set various algorithm-specific tuning parameters which are different from those used in traditional NLA. This paper demonstrates how a surrogate-based autotuning approach can be used to address fundamental problems of parameter selection in RandNLA algorithms. In particular, we provide a detailed investigation of surrogate-based autotuning for sketch-and-precondition (SAP)-based randomized least squares methods, which have been one of the great success stories in modern RandNLA. Empirical results show that our surrogate-based autotuning approach can achieve near-optimal performance with much less tuning cost than a random search (up to about 7.6x fewer trials of different parameter configurations). Moreover, while our experiments focus on least squares, our results demonstrate a general-purpose autotuning pipeline applicable to any kind of RandNLA algorithm.

Cho, Younghyun↗

DOE OSTI2025

Divertor Plasma Detachment Control Neural Network

DivControlNN is a state-of-the-art software tool that leverages advanced machine learning techniques to predict and control divertor plasma behavior in fusion reactors. Plasma, a highly energetic and electrically charged gas, requires meticulous management to protect reactor components and maintain optimal energy production. Conventional simulation methods, although extremely detailed, typically demand extensive computational time-making them unsuitable for real-time control scenarios. DivControlNN addresses this challenge by learning from tens of thousands of high-fidelity simulations, thereby creating a rapid surrogate model that can deliver near-instantaneous predictions. At the core of its functionality is a sophisticated technique known as latent space mapping, which condenses complex, high-dimensional plasma data into a compact, lower-dimensional representation. This streamlined representation enables the system to quickly forecast essential plasma properties and determine the precise conditions required for effective detachment. Detachment is a crucial process in which the plasma is cooled before reaching the divertor plates, thereby reducing heat loads and mitigating material erosion. In recent experiments conducted on the KSTAR tokamak in South Korea, DivControlNN successfully guided the detachment process without any fine-tuning-even when applied to a new tungsten divertor configuration. By achieving a computational speed-up of over one hundred million times compared to traditional simulation methods while maintaining low prediction errors, DivControlNN stands to significantly enhance real-time control and diagnostic capabilities in future fusion reactors. This breakthrough paves the way for safer, more reliable reactor operation and represents a major advancement toward realizing fusion energy as a practical, sustainable, and clean power source.

Xu, Xueqiao [Lawrence Livermore National Laborator↗

DOE OSTI2025

Ultracoherent SRF Cavity-Based Multi-Qudit Platform with Error-Resilient Control

Superconducting radio-frequency (SRF) cavities offer a promising platform for quantum computing due to their long coherence times, yet integrating nonlinear elements like transmons for control often introduces additional loss. We report a multimode quantum system based on a 2-cell elliptical shaped SRF cavity, comprising two cavity modes weakly coupled to an ancillary transmon circuit, designed to preserve coherence while enabling efficient control of the cavity modes. We mitigate the detrimental effects of the transmon decoherence through careful design optimization that reduces transmon-cavity couplings and participation in the dielectric substrate and lossy interfaces, to achieve single-photon lifetimes of 20.6\,ms and 15.6\,ms for the two modes, and a pure dephasing time exceeding 40\,ms. This marks an order-of-magnitude improvement over prior 3D multimode memories. Leveraging sideband interactions and novel error-resilient protocols, including measurement-based correction and post-selection, we achieve high-fidelity control over quantum states. This enables the preparation of Fock states up to $N = 20$ with fidelities exceeding 95\%, the highest reported to date to the authors' knowledge, as well as two-mode entanglement with an estimated coherence-limited fidelities of 99.9\% after post-selection. These results establish our platform as a robust foundation for quantum information processing, allowing for future extensions to high-dimensional qudit encodings.

Kim, T. [Northwestern U.]↗

DOE OSTI2026

Ultracoherent superconducting cavity-based multiqudit platform with error-resilient control

Superconducting radio-frequency (SRF) cavities offer a promising platform for quantum computing due to their long coherence times, yet integrating nonlinear elements like transmons for control often introduces additional loss. We report a multimode quantum system based on a 2-cell elliptical-shaped SRF cavity, comprising two cavity modes weakly coupled to an ancillary transmon circuit, designed to preserve coherence while enabling efficient control of the cavity modes. We mitigate the detrimental effects of the transmon decoherence through careful design optimization that reduces transmon-cavity couplings and participation in the dielectric substrate and lossy interfaces, to achieve single-photon lifetimes of 20.6 ms and 15.6 ms for the two modes, and a pure dephasing time exceeding 40 ms. This marks an order-of-magnitude improvement over prior 3D multimode memories. Leveraging sideband interactions and novel error-resilient protocols, including measurement-based correction and post-selection, we achieve high-fidelity control over quantum states. This enables the preparation of Fock states up to N = 20 with fidelities exceeding 95%, the highest reported to date to the authors' knowledge, as well as two-mode entanglement with an estimated coherence-limited fidelities of 99.9% after post-selection. These results establish our platform as a robust foundation for quantum information processing, allowing for future extensions to high-dimensional qudit encodings.

Lu, Yao [Fermilab] (ORCID:000000020413698X)↗

DOE OSTI2026

Ultracoherent superconducting cavity-based multiqudit platform with error-resilient control

Superconducting radio-frequency (SRF) cavities offer a promising platform for quantum computing due to their long coherence times, yet integrating nonlinear elements like transmons for control often introduces additional loss. We report a multimode quantum system based on a 2-cell elliptical-shaped SRF cavity, comprising two cavity modes weakly coupled to an ancillary transmon circuit, designed to preserve coherence while enabling efficient control of the cavity modes. We mitigate the detrimental effects of the transmon decoherence through careful design optimization that reduces transmon-cavity couplings and participation in the dielectric substrate and lossy interfaces, to achieve single-photon lifetimes of 20.6 ms and 15.6 ms for the two modes, and a pure dephasing time exceeding 40 ms. This marks an order-of-magnitude improvement over prior 3D multimode memories. Leveraging sideband interactions and novel error-resilient protocols, including measurement-based correction and post-selection, we achieve high-fidelity control over quantum states. This enables the preparation of Fock states up to N = 20 with fidelities exceeding 95%, the highest reported to date to the authors' knowledge, as well as two-mode entanglement with an estimated coherence-limited fidelities of 99.9% after post-selection. These results establish our platform as a robust foundation for quantum information processing, allowing for future extensions to high-dimensional qudit encodings.

Lu, Yao [Fermilab] (ORCID:000000020413698X)↗

DOE OSTI2025

Ultracoherent superconducting cavity-based multiqudit platform with error-resilient control

Superconducting radio-frequency (SRF) cavities offer a promising platform for quantum computing due to their long coherence times, yet integrating nonlinear elements like transmons for control often introduces additional loss. We report a multimode quantum system based on a 2-cell elliptical shaped SRF cavity, comprising two cavity modes weakly coupled to an ancillary transmon circuit, designed to preserve coherence while enabling efficient control of the cavity modes. We mitigate the detrimental effects of the transmon decoherence through careful design optimization that reduces transmon-cavity couplings and participation in the dielectric substrate and lossy interfaces, to achieve single-photon lifetimes of 20.6 ms and 15.6 ms for the two modes, and a pure dephasing time exceeding 40 ms. This marks an order-of-magnitude improvement over prior 3D multimode memories. Leveraging sideband interactions and novel error-resilient protocols, including measurement-based correction and post-selection, we achieve high-fidelity control over quantum states. This enables the preparation of Fock states up to $N = 20$ with fidelities exceeding 95%, the highest reported to date to the authors' knowledge, as well as two-mode entanglement with an estimated coherence-limited fidelities of 99.9% after post-selection. These results establish our platform as a robust foundation for quantum information processing, allowing for future extensions to high-dimensional qudit encodings.

Kim, Taeyoon [Fermilab; Northwestern U.]↗

DOE OSTI2025

Landscaper v1

Understanding the inner workings of machine learning models through their loss landscapes offers crucial insights into model properties, optimization dynamics, and generalizability. However, accessing these insights has traditionally required specialized mathematical expertise, limiting broader adoption. Landscaper is an open-source Python package designed to bridge this gap. Landscaper seamlessly integrates a suite of multi-dimensional loss landscape analyses with cutting-edge topological data analysis (TDA) methods. This powerful combination makes both fundamental loss landscape analysis and advanced TDA techniques accessible to the broader scientific ML community, without requiring deep pre-existing mathematical knowledge. Landscaper offers three key functionalities: * Construction: Builds detailed loss landscape representations through versatile low and high-dimensional sampling techniques. * Quantification: Applies advanced metrics, including a novel topological data analysis (TDA) based smoothness metric, enabling new perspectives on model behavior. * Visualization: Offers intuitive tools to visualize and interpret loss landscapes, providing actionable insights beyond traditional performance metrics.

Weber, Gunther [Lawrence Berkeley National Laborat↗

NASA NTRS1991

Design of optimal second-order state estimators

The present consideration of the design of online computation-saving second-order state estimators for second-order vector-matrix differential systems proposes a class of such estimators which is proven to possess guaranteed convergence. A class of optimal second-order estimators is then obtained, and the conditions required for optimality are identified. The estimator proposed offers high performance in conjunction with online computation reductions sufficiently great to allow the estimation of the large number of state variables associated with control of large, flexible space structures represented by high-dimensional second-order systems.

Joshi, Suresh M.↗

NASA NTRS2009

Physical Principle for Generation of Randomness

A physical principle (more precisely, a principle that incorporates mathematical models used in physics) has been conceived as the basis of a method of generating randomness in Monte Carlo simulations. The principle eliminates the need for conventional random-number generators. The Monte Carlo simulation method is among the most powerful computational methods for solving high-dimensional problems in physics, chemistry, economics, and information processing. The Monte Carlo simulation method is especially effective for solving problems in which computational complexity increases exponentially with dimensionality. The main advantage of the Monte Carlo simulation method over other methods is that the demand on computational resources becomes independent of dimensionality. As augmented by the present principle, the Monte Carlo simulation method becomes an even more powerful computational method that is especially useful for solving problems associated with dynamics of fluids, planning, scheduling, and combinatorial optimization. The present principle is based on coupling of dynamical equations with the corresponding Liouville equation. The randomness is generated by non-Lipschitz instability of dynamics triggered and controlled by feedback from the Liouville equation. (In non-Lipschitz dynamics, the derivatives of solutions of the dynamical equations are not required to be bounded.)

Zak, Michail↗

NASA NTRSDate not supplied

Enabling in-time Prognostics with Surrogate Modeling through Physics-enhanced Dynamic Mode Decomposition Method

Computational models provide essential quantitative tools for assessing and predicting the health and performance of physical systems. However, high-fidelity models are rarely used in real-time operations or large optimization loops, due to their time-intensive nature. A common approach to improving computational efficiency of prognosis is to employ surrogate models. Such models can significantly decrease computation time for some accuracy loss. In this context, use of Dynamic Mode Decomposition (DMD) is proposed to generate surrogate models for lithium-ion (Li-ion) battery discharge. DMD has been suggested and used successfully in the area of fluid dynamics for over a decade, but it has not been applied to the PHM domain, where far-ahead prediction of nonlinear behavior is crucial to propagate faults or predict Remaining Useful Life (RUL). For Li-ion battery health management, the standard application of DMD using only the observable quantities of interest was unable to capture the nonlinear discharge of batteries exhibited in lab testing. The Koopman theory, however, provides a mechanism to tradeoff low dimensional nonlinear models with high-dimensional linear ones in a DMD framework, by augmenting nonlinear state variables into the system representation. In this way, DMD allows for configurable simulation accuracy dependent on the dimensionality of the Koopman operator. For battery health management, we augmented the observable variables with the hidden states of a higher-fidelity physics model to build the DMD surrogate. In comparison to a high-fidelity model, the surrogate improved computational efficiency with only a minimal loss of accuracy, and enabled long-term prognostics horizons. A generalized method for this was implemented in the prog models python package.

prognostics and health management↗

NASA NTRS2022

Intrinsic Dimensionality as a Metric for the Impact of Mission Design Parameters

High-resolution space-based spectral imaging of the Earth's surface delivers critical information for monitoring changes in the Earth system as well as resource management and utilization. Orbiting spectrometers are built according to multiple design parameters, including ground sampling distance (GSD), spectral resolution, temporal resolution, and signal-to-noise ratio. Different applications drive divergent instrument designs, so optimization for wide-reaching missions is complex. The Surface Biology and Geology component of NASA's Earth System Observatory addresses science questions and meets applications needs across diverse fields, including terrestrial and aquatic ecosystems, natural disasters, and the cryosphere. The algorithms required to generate the geophysical variables from the observed spectral imagery each have their own inherent dependencies and sensitivities, and weighting these objectively is challenging. Here, we introduce intrinsic dimensionality (ID), a measure of information content, as an applications-agnostic, data-driven metric to quantify performance sensitivity to various design parameters. ID is computed through the analysis of the eigenvalues of the image covariance matrix, and can be thought of as the number of significant principal components. This metric is extremely powerful for quantifying the information content in high-dimensional data, such as spectrally resolved radiances and their changes over space and time. We find that the ID decreases for coarser GSD, decreased spectral resolution and range, less frequent acquisitions, and lower signal-to-noise levels. This decrease in information content has implications for all derived products. ID is simple to compute, providing a single quantitative standard to evaluate combinations of design parameters, irrespective of higher-level algorithms, products, applications, or disciplines.

Intrinsic dimensionality↗