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At least 217 records · Page 12

Optimal experimental design: Formulations and computations

Questions of ‘how best to acquire data’ are essential to modelling and prediction in the natural and social sciences, engineering applications, and beyond. Optimal experimental design (OED) formalizes these questions and creates computational methods to answer them. This article presents a systematic survey of modern OED, from its foundations in classical design theory to current research involving OED for complex models. We begin by reviewing criteria used to formulate an OED problem and thus to encode the goal of performing an experiment. We emphasize the flexibility of the Bayesian and decision-theoretic approach, which encompasses information-based criteria that are well-suited to nonlinear and non-Gaussian statistical models. We then discuss methods for estimating or bounding the values of these design criteria; this endeavour can be quite challenging due to strong nonlinearities, high parameter dimension, large per-sample costs, or settings where the model is implicit. A complementary set of computational issues involves optimization methods used to find a design; we discuss such methods in the discrete (combinatorial) setting of observation selection and in settings where an exact design can be continuously parametrized. Finally we present emerging methods for sequential OED that build non-myopic design policies, rather than explicit designs; these methods naturally adapt to the outcomes of past experiments in proposing new experiments, while seeking coordination among all experiments to be performed. Throughout, we highlight important open questions and challenges.

97 MATHEMATICS AND COMPUTING

A Kaczmarz-inspired approach to accelerate the optimization of neural network wavefunctions

Neural network wavefunctions optimized using the variational Monte Carlo method have been shown to produce highly accurate results for the electronic structure of atoms and small molecules, but the high cost of optimizing such wavefunctions prevents their application to larger systems. We propose the Subsampled Projected-Increment Natural Gradient Descent (SPRING) optimizer to reduce this bottleneck. SPRING combines ideas from the recently introduced minimum-step stochastic reconfiguration optimizer (MinSR) and the classical randomized Kaczmarz method for solving linear least-squares problems. We demonstrate that SPRING outperforms both MinSR and the popular Kronecker-Factored Approximate Curvature method (KFAC) across a number of small atoms and molecules, given that the learning rates of all methods are optimally tuned. For example, on the oxygen atom, SPRING attains chemical accuracy after forty thousand training iterations, whereas both MinSR and KFAC fail to do so even after one hundred thousand iterations.

97 MATHEMATICS AND COMPUTING

Best Methods for Fluoride Fuel Salt Dissolution and Digestion

This report serves as the deliverable for Milestone M4FT-26AN080502015 (Report on methodology for elemental/isotopic analysis of fluoride fuel salts). The review within this document is a summary of the current literature identified by Argonne regarding fluoride salt dissolution and digestion methods and provides guidance on selecting optimal fluoride dissolution and digestion methods for future fuel salt qualification studies. Methods are compared based on completeness of digestion, chemical hazards, and tradeoffs such as equipment needs or potential to introduce impurities. Recommendations are provided for best dissolution and digestion methods for uranium- and thorium-bearing salts, and ideas for key future experiments are described.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS

Practical and Optimal Sequential Bayesian Experimental Design for Complex Systems Incorporating Human Experimenter Preferences (Final Scientific/Technical Report)

Experiments are indispensable for developing models of complex systems. Carefully designed experiments can provide substantial savings for these expensive data-acquisition opportunities. However, designs based on heuristics are often suboptimal for systems with multiphysics, nonlinear dynamics, and uncertain and noisy environments. Optimal experimental design, while leveraging predictive models, seeks to systematically quantify and maximize the value of experiments. In this project, we focused on the design of multiple experiments, where current approaches are largely suboptimal: batch-design does not adapt to new data acquired during the experiment campaign (no feedback), and greedy/myopic design ignores future dynamics and consequences (no lookahead). We developed the mathematical framework and computational methods for sequential optimal experimental design (sOED) for complex systems. We enabled tractable model-based sOED in a rigorous manner through novel algorithms based on reinforcement learning, and investigated the effects of human experimenters on the design process. Our methods are fully Bayesian, able to quantify and update uncertainty in a principled manner. The traits aimed by our approach—mathematical rigor and optimality, human effects and uncertainty quantification, computational practicality—are crucial for elevating the standards of artificial intelligence (AI) to support decision-making in scientific domains, and contribute toward trust and realistic adoption of AI in experimental design practice.

97 MATHEMATICS AND COMPUTING

Elastic-wave sensitivity-guided adaptive seismic survey design for cost-effective monitoring of geological carbon storage

Effective seismic monitoring is essential for verifying CO₂ containment, detecting potential leakage, and optimizing operational decisions in geologic carbon storage. Here, this study presents a time-adaptive, elastic-wave sensitivity-guided framework for designing cost-effective seismic monitoring layouts for tracking CO₂ plume migration. The method is based on elastic-wave sensitivity analysis, which quantifies how variations in subsurface properties impact seismic wavefields. Two complementary design strategies are developed: one based on selecting a fixed number of seismic sources (Method A), and the other based on selecting source–receiver pairs contributing to a fixed fraction of cumulative elastic-wave sensitivity energy (Method B). The optimization workflow to identify source–receiver configurations with the highest detection potential is demonstrated using a hypothetical GCS scenario at the Kimberlina site in California using simulations of elastic-wave sensitivity data at multiple post-injection timesteps. Results show that both strategies adapt to evolving plume geometries and wavefield sensitivities, with Method B offering broader spatial coverage and Method A ensuring simpler deployment. This framework enables site-specific, cost-effective, and risk-informed seismic survey designs, enhancing the ability to monitor CO₂ migration over time in evolving geological environments

58 GEOSCIENCES

Optimization of Random Phase Approximation Calculations for Improved Energies of Molecules, Solids, and Surfaces

We present an optimized random phase approximation method (optRPA26) that significantly improves upon conventional RPA through an optimized choice of reference orbitals and energy components, rather than a modification of the RPA correlation functional itself. The method employs an empirically constructed hybrid functional to generate DFT orbitals to evaluate the RPA correlation energy, which is then scaled by a constant. Comprehensive benchmarks across molecules, bulk solids, and surface systems demonstrate that optRPA26 consistently achieves high accuracy, with mean absolute errors of 0.05 eV for W4-11-RE reaction energies, 0.07 eV for cohesive energies, 0.09 eV for metal oxide formation energies, 0.11–0.12 eV for adsorption of small molecules on metals, and 0.06 eV for adsorption on oxides. In addition, optRPA26 correctly captures phase stability in metal oxides and magnetic metals. The optRPA26 approach can be run using standard RPA implementations, highlighting its potential as a general-purpose reference method that can accurately capture covalent, ionic, metallic, and van der Waals bonding in molecules, solids, and interfaces.

Adsorption

Machine learning enhanced characterization and optimization of photonic cured MAPbI 3 for efficient perovskite solar cells

Photonic curing (PC) can facilitate high-speed perovskite solar cell (PSC) manufacturing because it uses high-intensity light pulses to crystallize perovskite films in milliseconds. However, optimizing PC conditions is challenging due to its many variables, and using power conversion efficiency (PCE) as the optimization metric is both time-consuming and labor-intensive. This work presents a machine learning (ML) approach to optimize PC conditions for fabricating methylammonium lead iodide (MAPbI 3 ) films by quantitatively comparing their ultraviolet-visible (UV-vis) absorbance spectra to thermal annealed (TA) films using four similarity metrics. We perform Bayesian optimization coupled with Gaussian process regression (BO-GP) to minimize the similarity metrics. Refining PC conditions using active learning based on BO-GP models, we achieve a PC MAPbI3 film with an absorbance spectrum closely matching a TA reference film, which is further verified by its crystalline and morphological properties. Thus, we demonstrate that the UV-vis absorption spectrum can accurately proxy film quality. Additionally, we use an AI-based segmentation model for a more efficient grain size analysis. However, when we use the optimized PC condition to fabricate PSCs, we find that interaction between MAPbI 3 and the hole transport layer (HTL) during PC critically degrades the PSC performance. By adding a buffer layer between the HTL and MAPbI 3 , the optimized PC PSCs produce a champion PCE of 11.8%, comparable to the TA reference of 11.7%. Using UV-vis similarity metrics instead of device PCE as the objective in our BO-GP method accelerates the optimization of PC processing conditions for MAPbI 3 films.

14 SOLAR ENERGY

Method Validation Summary for L16.2 AD-ISO-0015 for ISO-17025 / NFAC Applications

Methods for the analysis of semi-volatile organic compounds are employed at Savannah River National Laboratory (SRNL) for routine and non-routine samples from tank waste, process control, waste acceptance, and a wide array of other process and research samples. A method has been developed by SRNL, based on existing methods for semi-volatile analysis, for the analysis of nitroaromatic high explosives by gas chromatography / mass spectrometry in soils and sediments. Relative to past work performed at SRNL on nitroaromatic explosives, this developed, optimized, and validated method can achieve lower limits of detection and quantitation, greater precision, lower bias, higher linearity, and accuracy across a greater linear range.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W

INTEGRATION OF DATA ANALYTICS WITH SYSTEM HEALTH PROGRAMS

Industry equipment reliability and asset management programs are essential elements that help ensure the safe and economical operation of nuclear power plants. The effectiveness of these programs is addressed in several industry developed and regulatory programs. However, these programs have proven to be labor intensive and expensive. There is an opportunity to significantly enhance the collection, analysis, and use of this information to provide more cost-effective plant operation. Additionally, there is an acute industry need to leverage advanced technology to reduce costs and improve operational effectiveness. The goal of this paper is to provide effective and efficient analytical methods and tools to support risk-informed decisions for the equipment reliability and asset management programs at nuclear power plants. This is accomplished by creating a direct bridge between component health/lifecycle data and decision making (e.g., maintenance scheduling and project prioritization). Here we are supporting typical system engineer decisions regarding maintenance activity scheduling and component ageing management. This is performed in a risk-informed context where herein the term “risk” is broadly constructed to include both plant reliability and economics. This framework combines data analytics tools to analyze equipment reliability data with risk-informed methods designed to support system engineer decisions (e.g., maintenance and replacement schedules, optimal maintenance posture) in a customizable workflow. A challenge is that the structure of this workflow strongly depends on the decision that needs to be made, the type of data available, and the constraints that need to be considered. Current methods are designed to provide specific answers to specific problems; however, these methods might prove to be inadequate even when problem settings slightly change (e.g., different types of requirements, additional dependencies between system reliability and economics). We tackled this challenge by designing framework in a flexible and modular fashion such that the user can assemble and customize his/her own workflow that integrates SSC economic lifecycle models (e.g., maintenance and replacement costs), system reliability models, and optimization methods.

97 - MATHEMATICS AND COMPUTING

Integrating novel stellarator single-stage optimization algorithms to design the Columbia stellarator experiment

Abstract The Columbia Stellarator eXperiment (CSX), currently being designed at Columbia University, aims to test theoretical predictions related to QA plasma behavior, and to pioneer the construction of an optimized stellarator using three-dimensional, non-insulated high-temperature superconducting (NI-HTS) coils. The magnetic configuration is generated by a combination of two circular planar poloidal field (PF) coils and two 3D-shaped interlinked (IL) coils, with the possibility to add windowpane coils to enhance shaping and experimental flexibility. The PF coils and vacuum vessel are repurposed from the former Columbia Non-Neutral Torus experiment, while the IL coils will be custom-wound in-house using NI-HTS tapes. To obtain a plasma shape that meets the physics objectives with a limited number of coils, novel single-stage optimization techniques are employed, optimizing both the plasma and coils concurrently, in particular targeting a tight aspect ratio QA plasma and minimized strain on the HTS tape. Despite the increased complexity due to the expanded degrees of freedom, these methods successfully identify optimized plasma geometries that can be realized by coils meeting engineering specifications. This paper discusses the derivation of the constraints and objectives specific to CSX, and describe how two recently developed single-stage optimization methodologies are applied to the design of CSX. A set of selected configurations for CSX is then described in detail.

Baillod, A. (ORCID:0000000303529180)

Networked Microgrids Optimization

This project is mainly about the operation optimization of three networked microgrids (MG), including centralized optimization and distributed optimization. The alternating direction method of multipliers (ADMM) algorithm is used for distributed optimization. In the distribution network considered here, there is a Distribution Management system (DMS) as the system coordinator and several networked microgrids. In grid-connected mode, power could be imported or exported at the distribution substation bus according to the utility rate, and the exchanged power at point of common coupling (PCC) of any microgrid has a limitation. In islanded mode, the power imports/exports at the distribution substation are zero. In both grid-connected and islanded mode, the distribution substation is taken as a slack bus with fixed voltage magnitude.

Chen, Yang [Oak Ridge National Laboratory (ORNL),

Efficient online quantum circuit learning with no upfront training

Optimization is a promising candidate for studying the utility of variational quantum algorithms (VQAs). However, evaluating cost functions using quantum hardware introduces runtime overheads that limit exploration. Surrogate-based methods can reduce calls to a quantum computer, yet existing approaches require hyperparameter pre-training and have been tested only on small problems. Here, we show that surrogate-based methods can enable successful optimization at scale, without pre-training, by using radial basis function interpolation (RBF) to construct an adaptive, hyperparameter-free surrogate. Using the surrogate as an acquisition function drives hardware queries to the vicinity of the true optima. For 16-qubit random 3-regular Max-Cut instances with the Quantum Approximate Optimization Algorithm (QAOA), our method outperforms state-of-the-art approaches, without considering their upfront training costs. Furthermore, we successfully optimize QAOA circuits for 127-qubit random Ising models on an IBM processor using 10 4 −10 5 measurements. Strong empirical performance demonstrates the promise of automated surrogate-based learning for large-scale VQA applications.

97 MATHEMATICS AND COMPUTING

A method for bounding high-order finite element functions: Applications to mesh validity and bounds-preserving limiters

We introduce a novel method for bounding high-order multi-dimensional polynomials in finite element approximations. The method involves precomputing optimal piecewise-linear bounding boxes for polynomial basis functions, which can then be used to locally bound any combination of these basis functions. This approach can be applied to any element/basis type at any approximation order, can provide local (i.e., subcell) extremum bounds to a desired level of accuracy, and can be evaluated efficiently on-the-fly in simulations. Furthermore, we show that this approach generally yields more accurate bounds in comparison to traditional methods based on convex hull properties (e.g., Bernstein polynomials). Furthermore, the efficacy of this technique is shown in applications such as mesh validity checks and optimization for high-order curved meshes, where positivity of the element Jacobian determinant can be ensured throughout the entire element, and continuously bounds-preserving limiters for hyperbolic systems, which can enforce maximum principle bounds across the entire solution polynomial.

Bounding box

Nonadiabatic Force Matching for Alchemical Free-Energy Estimation

We propose a method to compute free-energy differences from nonadiabatic alchemical transformations by using flow-based generative models. The method, nonadiabatic force matching, hinges on estimating the dissipation along an alchemical switching process in terms of a nonadiabatic force field that can be learned through stochastic flow matching. The learned field can be used in conjunction with short-time trajectory data to evaluate upper and lower bounds on the alchemical free energy that variationally converge to the exact value if the field is optimal. Applying the method to evaluate the alchemical free energy of atomistic models shows that it can substantially reduce the simulation cost of a free-energy estimate at a negligible loss of accuracy when compared with thermodynamic integration.

Computational chemistry

Optimal Transport as a Tool for Scientific Discovery in Radiation Biology

This report summarizes findings from research conducted for the “Exploration of the Poten tial for Artificial Intelligence and Machine Learning to Advance Low-Dose Radiation Biology Re search” (RadBio-AI) program, supported by the U.S. Department of Energy, Office of Science, Office of Biological and Environmental Research, under Awards KP1601011/FWP CC121 and KP1601017/FWP CC121. The research reported here was undertaken in an effort to assess the potential of optimal measure transport methods as components within the larger scope of a com putational framework envisioned to support research in the radiation biology domain. Within this effort, our interest centered on enabling a unified generic framework where probabilistic modeling, inference, and statistical learning can be carried out for a wide range of data distributions. As described next in Section 1 (and in more detail in our original publication), optimal measure transport offers the possibility of such unified approach.

97 MATHEMATICS AND COMPUTING

A Smoothed Augmented Lagrangian Framework for Convex Optimization with Nonsmooth Constraints

Augmented Lagrangian (AL) methods have proven remarkably useful in solving optimization problems with complicated constraints. The last decade has seen the development of overall complexity guarantees for inexact AL variants. Yet, a crucial gap persists in addressing nonsmooth convex constraints. To this end, we present a smoothed augmented Lagrangian (AL) framework where nonsmooth terms are progressively smoothed with a smoothing parameter $\eta _k$ . The resulting AL subproblems are $\eta _k$ -smooth, allowing for leveraging accelerated schemes. By a careful selection of the inexactness level $\epsilon _k$ (for inexact subproblem resolution), the penalty parameter $\rho _k$ , and smoothing parameter $\eta _k$ at epoch k, we derive rate and complexity guarantees of $\tilde{\mathcal {O}}(1/{\varepsilon }^{3/2})$ and $\tilde{\mathcal {O}}(1/{\varepsilon })$ in convex and strongly convex regimes for computing an ${\varepsilon }$ -optimal solution, when $\rho _k$ increases at a geometric rate, a significant improvement over the best available guarantees for AL schemes for convex programs with nonsmooth constraints. Analogous guarantees are developed for settings with $\rho _k = \rho$ as well as $\eta _k = \eta$ . Preliminary numerics on a fused Lasso problem display promise.

augmented Lagrangian

Bayesian prior construction for uncertainty quantification in first-principles statistical mechanics

First-principles statistical mechanics enables the prediction of thermodynamic and kinetic properties of materials, but is computationally expensive. Many approaches require surrogate models to calculate energies within Monte Carlo or molecular dynamics simulations. Inexpensive surrogates such as cluster expansions enable otherwise intractable calculations by interpolating data from higher accuracy methods, such as Density Functional Theory (DFT). Surrogate models introduce uncertainty into downstream calculations, in addition to any uncertainty inherent to DFT calculations. Bayesian frameworks address this by quantifying uncertainty and incorporating expert knowledge through priors. However, constructing effective priors remains challenging. This work introduces and describes practical strategies for building Bayesian cluster expansions, focusing on basis truncation, hyperparameter selection, and ground state replication. We analyze multiple basis truncation schemes, compare cross-validation to the evidence-approximation for hyperparameter optimization, and provide methods to find and enforce ground-state-preserving models through priors. Additionally, we compare the uncertainties between different approximations to DFT (LDA, PBE, SCAN) against the uncertainty introduced with the use of cluster expansion surrogate models. These approaches are demonstrated on the BCC Li x Mg 1-x and Li x Al 1-x alloys, which are both of interest for solid-state Li batteries. Our results provide guidelines for constructing and utilizing Bayesian cluster expansions, thereby improving the transparency of materials modeling. Furthermore, the approaches and insights developed in this work can be transferred to a wide range of cluster expansion surrogate models, including the atomic cluster expansion and related machine-learned interatomic potential architectures.

Alloy theory

Economic dispatch of offshore renewable energy resources for islanded communities with optimal storage sizing

Coastal or isolated microgrids depend on diesel generators and could benefit from renewable energy resources, especially offshore wind and wave energy. Integrating these resources into microgrids is complicated by their high intermittency, which requires optimal economic dispatch to effectively evaluate. This study considers three coastal or islanded sites, and uses mid-fidelity models of wind and wave energy technologies, and local demand data to solve the optimal economic dispatch problem. An optimal storage sizing method is developed that finds the smallest capacity of energy storage required to meet the microgrid load during each season. The storage capacity decreases by a factor of two at most when adding wave energy converters to a system. Adding wave energy converters to a farm decreases cost by about 30%. Furthermore, the required storage size varies by two to three times from summer to winter. Compared with the state-of-the-art approaches that often overlook realistic offshore renewable energy technology in microgrid economic dispatch and optimal storage sizing, the proposed solution introduced in this study allows for better site selection, microgrid design, converter selection, and storage sizing considerations for isolated microgrids.

16 TIDAL AND WAVE POWER