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At least 379 records · Page 21

Improved loss functions for machine-learned atomic potentials

Machine learning (ML) has become an invaluable tool across a wide array of domains in science as researchers find new ways to leverage its predictive power. This is especially true in chemistry, where ML is used to fit chemical properties or desirable attributes to the local structure of molecules and materials. In the pursuit of greater accuracy, it is relatively simple to increase the size or complexity of such models, although this often requires simultaneously seeking larger datasets in order to both fit and interpret the larger number of parameters. However, it is equally important to assess the quality and relative importance of the data and how these factors impact the training process. We, therefore, investigate the impact of using different loss functions for training neural network potentials (NNPs), as the loss function defines the error and parameter gradients used to train the NNP. In particular, we test the mean-squared error and Huber loss functions and, using insight from these functions, derive a new loss function based on the Asinh function, which yields significant improvement in the accuracy and generality of NNPs. We show that by discounting/minimizing errors and anomalies in the optimization process, both the Huber and Asinh loss functions improve the training of NNPs, leading to a final potential with a greater effective dimensionality.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Collaborative Research: Enabling multi-scale studies of magnetic reconnection with interpretable data-driven models

The development of accurate reduced descriptions and improved closures for magnetic reconnection is an important and a long‐standing challenge in plasma physics. The four‐fluid approach, and associated closures, that were investigated have the potential to improve the accuracy of plasma fluid models, capturing physical effects which would otherwise require a kinetic description. If successful, this approach could have an important impact for the modeling of laboratory and space plasmas. The major goals of this project were to develop new machine learning (ML) tools based on sparse and symbolic regression techniques, and to extract interpretable and generalizable reduced models (e.g., in the form of partial differential equations - PDEs) from data generated by first principles plasma simulations. Preserving interpretability of such data‐driven models is key to addressing the long‐standing theoretical and numerical challenges. Prior proof‐of‐principle studies have demonstrated the enormous potential of this approach, by recovering the well‐established hierarchy of plasma equations (from Vlasov to MHD) from data produced by particle‐in‐cell (PIC) simulations. Our goal in this project was to extend and apply these new tools to construct better kinetic closures for magnetic reconnection; to derive better models of particle injection and acceleration by this fundamental plasma process; and to use this understanding to accelerate the development of multi‐scale plasma algorithms. While our immediate focus was on the problem of magnetic reconnection, the tools that were will developed are general and applicable to other areas of plasma physics, and more broadly to many‐body phenomena. We anticipate that the development of these multi‐scale models will have a significant impact across different areas of plasma science, from fusion to space and astrophysical plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Data-Centric Operational Design Domain Characterization for Machine Learning-Based Aeronautical Products

We give for Machine Learning (ML)-based aeronautical products, a first rigorous characterization of Operational Design Domains (ODDs). Unlike in other application sectors (such as self-driving road vehicles) where ODD development is scenario-based, our approach is data-centric: we propose the dimensions along which the parameters that define an ODD can be explicitly captured, using a top-down approach starting from system specifications, and a bottom-up approach starting from detailed ML Model (MLM) designs. Then we give a categorization of the data that ML-based applications can encounter in operation, identifying their system-level relevance and impact. Specifically, we discuss how those data categories are useful to determine: (1) the requirements necessary to drive the design of MLMs; (2) the potential effects on the MLM and higher levels of the system hierarchy; (3) the learning assurance processes that may be needed, and (4) system architectural considerations. We illustrate the underlying concepts with an example of an aircraft flight envelope. The approach in this paper is one of the cornerstones of a future process guidance for development and certification/approval of safety-related aeronautical products implementing Artificial Intelligence (AI), currently being developed through aviation industry-based consensus, jointly by the SAE G-34 Committee for AI in aviation, and EUROCAE WG-114 for AI.

Aeronautical products↗

Open data sets for assessing photovoltaic system reliability

Photovoltaic (PV) systems have become a cornerstone of renewable energy strategies, particularly due to the significant reduction in solar power costs over the past decade. However, the long-term reliability of PV installations presents a persistent challenge, requiring the development of advanced monitoring and predictive maintenance strategies. A wide range of data types is used to evaluate the health of PV systems, including environmental conditions, electrical performance, and inspection imagery. These data enable methodologies such as machine learning (ML) models for lifetime prediction and computer vision techniques for defect detection. However, the acquisition of high-quality and comprehensive data is difficult, particularly in terms of long-term consistency and data variety. Publicly available data sets serve as valuable resources for addressing these challenges, but they often suffer from fragmentation and are difficult to access. This paper presents a comprehensive review of existing open-source data sets related to PV degradation, analyzing their features, functionalities, and potential applications. We categorize these data sets based on the specific aspects of PV system information they cover, such as environmental conditions, operational monitoring, image inspection and module materials, and propose relevant tools and ML models for processing them. In addition, we propose practices for future data collection and usage, while also discussing potential directions in data-driven research. Our aim is to enhance data utilization and publication among researchers and industry professionals, promoting a deeper understanding of the role of data in enhancing the performance and durability of PV systems.

14 SOLAR ENERGY↗

Computational tools and data integration to accelerate vaccine development: challenges, opportunities, and future directions

The development of effective vaccines is crucial for combating current and emerging pathogens. Despite significant advances in the field of vaccine development there remain numerous challenges including the lack of standardized data reporting and curation practices, making it difficult to determine correlates of protection from experimental and clinical studies. Significant gaps in data and knowledge integration can hinder vaccine development which relies on a comprehensive understanding of the interplay between pathogens and the host immune system. In this review, we explore the current landscape of vaccine development, highlighting the computational challenges, limitations, and opportunities associated with integrating diverse data types for leveraging artificial intelligence (AI) and machine learning (ML) techniques in vaccine design. We discuss the role of natural language processing, semantic integration, and causal inference in extracting valuable insights from published literature and unstructured data sources, as well as the computational modeling of immune responses. Furthermore, we highlight specific challenges associated with uncertainty quantification in vaccine development and emphasize the importance of establishing standardized data formats and ontologies to facilitate the integration and analysis of heterogeneous data. Through data harmonization and integration, the development of safe and effective vaccines can be accelerated to improve public health outcomes. Looking to the future, we highlight the need for collaborative efforts among researchers, data scientists, and public health experts to realize the full potential of AI-assisted vaccine design and streamline the vaccine development process.

60 APPLIED LIFE SCIENCES↗

Throughput Estimation of Data Transport Networks From Digital Twin Measurements

Digital twins of networked infrastructures, known as Virtual Infrastructure Twins (VITs), are increasingly used for software development, pre-deployment testing, and design space exploration. While VITs avoid the costs and potential disruptions associated with experiments on operational networks, their throughput measurements are typically not sufficiently accurate for performance profiling of wide-area networks that they emulate. Here, machine learning (ML) methods are developed to transform these inaccurate VIT network throughput measurements to closely match in peak and overall profile of those from a physical testbed or production network. First, a micro kernel network reflecting a physical network is utilized to collect one-time measurements on a host to support this ML transformation. Then, a generic multi-modal ML method is developed to learn a map that transforms measurements from subsequent VITs on the same host to match past, current and follow-on testbed and cloud networks. ML generalization equations are derived to establish its correctness and probabilistically guarantee its generalization accuracy. Experimental results are presented for a variety of VIT hosts with target testbed and cloud networks; they include a case study of a four-site science ecosystem wherein inaccurate convex VIT measurement profiles are transformed into accurate concave profiles of target networks.

97 MATHEMATICS AND COMPUTING↗

Revealing the evolution of order in materials microstructures using multi-modal computer vision

The development of high-performance materials for microelectronics, energy storage, and extreme environments depends on our ability to describe and direct property-defining microstructural order. Our present understanding is typically derived from laborious manual analysis of imaging and spectroscopy data, which is difficult to scale, challenging to reproduce, and lacks the ability to reveal latent associations needed for mechanistic models. Here, we demonstrate a multi-modal machine learning (ML) approach to describe order from electron microscopy analysis of the complex oxide La 1−x Sr x FeO 3 . We construct a hybrid pipeline based on fully and semi-supervised classification, allowing us to evaluate both the characteristics of each data modality and the value each modality adds to the ensemble. We observe distinct differences in the performance of uni- and multi-modal models, from which we draw general lessons in describing crystal order using computer vision.

36 MATERIALS SCIENCE↗

Machine learning-enhanced MPC for demand flexibility in small commercial buildings: An experimental study

Small- and medium-sized commercial buildings (SMCBs) represent the majority of U.S. commercial building stock and a significant share of peak electricity demand, yet they often lack centralized building automation systems, representing a significant untapped resource for urban energy management. This infrastructure gap makes advanced control implementation challenging, limiting the potential for widespread demand flexibility. Model Predictive Control (MPC) has shown strong potential for load shifting, peak demand reduction, and cost savings, but its effectiveness is hindered by unmeasured disturbances such as internal heat gains. This paper presents a Hybrid MPC framework that integrates a physics-based gray-box building thermal model, identified using a lumped disturbance (LD) approach, with a machine learning (ML) model for forecasting unmeasured disturbances. The hybrid approach is designed for buildings with multiple individually controlled heat pump and thermostat pairs, common in SMCBs, and aims to optimize coordinated scheduling of multiple heat pumps under dynamic electricity pricing while respecting comfort constraints. The methodology is validated through both simulations of case study buildings and experimental studies at a highly-instrumented test facility. Simulation results show that the Hybrid MPC achieves substantial load shifting and peak demand reduction, approaching the performance of an ideal MPC with perfect disturbance knowledge, and outperforming a conventional MPC without disturbance forecasting. In experiments, the Hybrid MPC reduced daily HVAC energy costs by 8.7%, peak-price time load (load shifting) by 41.7%, and peak demand by 29.2% compared to baseline control, demonstrating comparable benefits to the 11.6% cost savings, 42.9% load shifting, and 23.2% peak reduction of the ideal MPC. These results demonstrate that the proposed hybrid modeling approach can significantly improve MPC performance in real-world SMCB applications without requiring additional disturbance measurements.

Demand Flexibility↗

Anomalous electroweak physics unraveled via evidential deep learning

The ever-growing ecosystem of beyond standard model (BSM) calculations and parametrizations has motivated the development of systematic methods for making quantitative cross-comparisons over the wide range of possible models, especially with controllable uncertainties. In this setting, the language of uncertainty quantification (UQ) furnishes useful metrics for assessing statistical overlaps and discrepancies among BSM and related models. In this study, we leverage recent machine learning (ML) developments in evidential deep learning (EDL) for UQ to separate data (aleatoric) and knowledge (epistemic) uncertainties in a model-discrimination setting. We construct several potentially BSM-motivated scenarios for the anomalous electroweak interaction (AEWI) of neutrinos with nucleons in deep inelastic scattering ( v DIS). These scenarios are then quantitatively mapped, as a demonstration, alongside Monte Carlo replicas of the CT18 PDFs used to calculate the $\varDelta \chi ^{2}$ statistic for a typical multi-GeV v DIS experiment, CDHSW. Our framework effectively highlights areas of model agreement and provides a classification of out-of-distribution (OOD) samples. By offering the opportunity to quantitatively understand model overlaps, the approach presented in this work can help facilitate efficient BSM model exploration and exclusion for future New Physics searches.

AI↗

A Data-Agnostic, Continuous Machine Learning Framework for Application in High Energy Physics and Beyond: Phase 1 Final Scientific/Technical Report

This Phase 1 effort has focused on the development of continual learning frameworks for use in machine learning, specifically in the applied context of High Energy Physics (HEP). Machine learning (ML) is a transformative technology by which computers, typically through the use of neural networks, are able to perform tasks with proficiency that rivals or surpasses that of human users. Model Degradation & Catastrophic Forgetting are two undesired phenomena which can occur in ML where the performance of a model degrades when either deployed on novel data streams, or trained on novel data which are sufficiently different than the data the models were initially trained on. A natural example where these sorts of effects can be observed is in the performance of detectors in harsh environments, where the detector signature may change over the lifetime of the detector as it ages and deteriorates — precisely what occurs in the experiments conducted in HEP. Real world HEP data is therefore an excellent test-ground and use-case for Continual Learning paradigms, which are techniques used in ML to counteract these problems. Ensemble learning is one such technique, where multiple smaller models are trained on subsets of the overall data and are ensembled together during inference. The intuition behind this technique is that, although there are shifts in the distributions which govern the incoming data streams, these shifts are not expected to be homogeneous or global. If a sufficient diversity in solutions within the various sub-models has been achieved, then at least one sub-model is expected to retain its performance within the overall ensemble. One further strength of this approach is that the architectures of the various models do not need to be identical, and in fact even different modalities of data can naturally be combined in this way. This work focused on applying ensemble learning techniques to derive results using two main datasets, anomaly detection in HEP data & time-series forecasting in semiconductor manufacturing data. Semiconductor manufacturing involves data with surprising similarity to that of HEP (e.g. wafer maps look very similar to digi-occupancy maps) and Cerium Lab’s prominence within the semiconductor industry makes semiconductor manufacturing a natural opportunity for commercialization of this work. Our efforts have led to two strong results. The first is that we evaluated the proposed ensembling techniques using previously proposed machine learning architectures for use in anomaly detection, namely AutoEncoder based models and their derivatives. We also developed new architectures which have not been evaluated in this context before. In fact, this work marks the first use of Vision Transformers for anomaly detection in HEP. Second, we demonstrated that ensemble learning significantly improves model performance in scenarios prone to degradation, validating its effectiveness across both HEP and semiconductor datasets. These results further support ensemble learning as a powerful strategy for mitigating catastrophic forgetting and maintaining robust performance in evolving data environments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Real-time tracking of structural evolution in 2D MXenes using theory-enhanced machine learning

In situ Electron Energy Loss Spectroscopy (EELS) combined with Transmission Electron Microscopy (TEM) has traditionally been pivotal for understanding how material processing choices affect local structure and composition. However, the ability to monitor and respond to ultrafast transient changes, now achievable with EELS and TEM, necessitates innovative analytical frameworks. Here, we introduce a machine learning (ML) framework tailored for the real-time assessment and characterization of in operando EELS Spectrum Images (EELS-SI). We focus on 2D MXenes as the sample material system, specifically targeting the understanding and control of their atomic-scale structural transformations that critically influence their electronic and optical properties. This approach requires fewer labeled training data points than typical deep learning classification methods. By integrating computationally generated structures of MXenes and experimental datasets into a unified latent space using Variational Autoencoders (VAE) in a unique training method, our framework accurately predicts structural evolutions at latencies pertinent to closed-loop processing within the TEM. This study presents a critical advancement in enabling automated, on-the-fly synthesis and characterization, significantly enhancing capabilities for materials discovery and the precision engineering of functional materials at the atomic scale.

47 OTHER INSTRUMENTATION↗

NANO.PTML model for read-across prediction of nanosystems in neurosciences. computational model and experimental case of study

Abstract Neurodegenerative diseases involve progressive neuronal death. Traditional treatments often struggle due to solubility, bioavailability, and crossing the Blood-Brain Barrier (BBB). Nanoparticles (NPs) in biomedical field are garnering growing attention as neurodegenerative disease drugs (NDDs) carrier to the central nervous system. Here, we introduced computational and experimental analysis. In the computational study, a specific IFPTML technique was used, which combined Information Fusion (IF) + Perturbation Theory (PT) + Machine Learning (ML) to select the most promising Nanoparticle Neuronal Disease Drug Delivery (N2D3) systems. For the application of IFPTML model in the nanoscience, NANO.PTML is used. IF-process was carried out between 4403 NDDs assays and 260 cytotoxicity NP assays conducting a dataset of 500,000 cases. The optimal IFPTML was the Decision Tree (DT) algorithm which shown satisfactory performance with specificity values of 96.4% and 96.2%, and sensitivity values of 79.3% and 75.7% in the training (375k/75%) and validation (125k/25%) set. Moreover, the DT model obtained Area Under Receiver Operating Characteristic (AUROC) scores of 0.97 and 0.96 in the training and validation series, highlighting its effectiveness in classification tasks. In the experimental part, two samples of NPs (Fe 3 O 4 _A and Fe 3 O 4 _B) were synthesized by thermal decomposition of an iron(III) oleate (FeOl) precursor and structurally characterized by different methods. Additionally, in order to make the as-synthesized hydrophobic NPs (Fe 3 O 4 _A and Fe 3 O 4 _B) soluble in water the amphiphilic CTAB (Cetyl Trimethyl Ammonium Bromide) molecule was employed. Therefore, to conduct a study with a wider range of NP system variants, an experimental illustrative simulation experiment was performed using the IFPTML-DT model. For this, a set of 500,000 prediction dataset was created. The outcome of this experiment highlighted certain NANO.PTML systems as promising candidates for further investigation. The NANO.PTML approach holds potential to accelerate experimental investigations and offer initial insights into various NP and NDDs compounds, serving as an efficient alternative to time-consuming trial-and-error procedures.

60 APPLIED LIFE SCIENCES↗

Recommendations for Comprehensive and Independent Evaluation of Machine Learning‐Based Earth System Models

Abstract Machine learning (ML) is a revolutionary technology with demonstrable applications across multiple disciplines. Within the Earth science community, ML has been most visible for weather forecasting, producing forecasts that rival modern physics‐based models. Given the importance of deepening our understanding and improving predictions of the Earth system on all time scales, efforts are now underway to develop Earth‐system models (ESMs) capable of representing all components of the coupled Earth system (or their aggregated behavior) and their response to external changes over long timescales. Building trust in ESMs is a much more difficult problem than for weather forecast models, not least because the model must represent the alternate (e.g., future or paleoclimatic) coupled states of the system for which there are no direct observations. Given that the physical principles that enable predictions about the response of the Earth system are often not explicitly coded in these ML‐based models, demonstrating the credibility of ML‐based ESMs thus requires us to build evidence of their consistency with the physical system. To this end, this paper puts forward five recommendations to enhance comprehensive, standardized, and independent evaluation of ML‐based ESMs to strengthen their credibility and promote their wider use.

54 ENVIRONMENTAL SCIENCES↗

Portable Acceleration of CMS Computing Workflows with Coprocessors as a Service

Computing demands for large scientific experiments, such as the CMS experiment at the CERN LHC, will increase dramatically in the next decades. To complement the future performance increases of software running on central processing units (CPUs), explorations of coprocessor usage in data processing hold great potential and interest. Coprocessors are a class of computer processors that supplement CPUs, often improving the execution of certain functions due to architectural design choices. We explore the approach of Services for Optimized Network Inference on Coprocessors (SONIC) and study the deployment of this as-a-service approach in large-scale data processing. In the studies, we take a data processing workflow of the CMS experiment and run the main workflow on CPUs, while offloading several machine learning (ML) inference tasks onto either remote or local coprocessors, specifically graphics processing units (GPUs). With experiments performed at Google Cloud, the Purdue Tier-2 computing center, and combinations of the two, we demonstrate the acceleration of these ML algorithms individually on coprocessors and the corresponding throughput improvement for the entire workflow. This approach can be easily generalized to different types of coprocessors and deployed on local CPUs without decreasing the throughput performance. We emphasize that the SONIC approach enables high coprocessor usage and enables the portability to run workflows on different types of coprocessors.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

A hybrid numerical and machine learning framework for evaluating the performance of a 780 cm 2 aqueous organic redox flow battery

Aqueous organic redox flow battery (AORFB) is a promising cost-competitive technology for large-scale energy storage. Among existing work, the dihydroxyphenazine (DHP)-based AORFB has demonstrated high energy density and low capacity degradation in 10 cm2 cells during lab tests. However, its commercial-scale performance in more complex environments remains unknown, posing a barrier for commercialization. To address this gap, this work presents a comprehensive performance evaluation of a 780 cm 2 DHP-based AORFB by combining physics-based numerical model, machine learning (ML)-based surrogate models, and ML-derived sensitivity quantification. Specifically, we first select 12 key battery parameters that include 10 physicochemical quantities and 2 operation quantities, then select 6 performance metrics that include energy efficiency (EE), discharging capacity, charging energy, and power losses due to concentration, activation, and ohmic over-potentials. With such selection, 12800 combinations of the 12 parameters are subsequently generated using the Latin Hypercube Sampling method. These combinations, together with 38 pre-defined State of Charge, are then integrated to a validated AORFB model developed in COMSOL to compute the performance metrics. With both input parameters and performance metrics, 60 deep neural network (DNN) surrogate models are then trained to approximate the relationship between the 10 physicochemical quantities and 6 performance metrics at each flow rate and current density. Sensitivity scores are then calculated based on the DNN models. Two additional sensitivity analysis tools, i.e., MARS, and SHAP, are also used to cross-validate the sensitivity scores from the DNN. The results demonstrate that 1) the standard potential ranks the first in controlling EE and charging energy, 2) the membrane conductivity is most critical for power loss and EE, and 3) specific area and reaction rate control activation power loss.

25 ENERGY STORAGE↗

Transforming Agricultural Productivity with AI-Driven Forecasting: Innovations in Food Security and Supply Chain Optimization

Global food security is under significant threat from climate change, population growth, and resource scarcity. This review examines how advanced AI-driven forecasting models, including machine learning (ML), deep learning (DL), and time-series forecasting models like SARIMA/ARIMA, are transforming regional agricultural practices and food supply chains. Through the integration of Internet of Things (IoT), remote sensing, and blockchain technologies, these models facilitate the real-time monitoring of crop growth, resource allocation, and market dynamics, enhancing decision making and sustainability. The study adopts a mixed-methods approach, including systematic literature analysis and regional case studies. Highlights include AI-driven yield forecasting in European hydroponic systems and resource optimization in southeast Asian aquaponics, showcasing localized efficiency gains. Furthermore, AI applications in food processing, such as plasma, ozone and Pulsed Electric Field (PEF) treatments, are shown to improve food preservation and reduce spoilage. Key challenges—such as data quality, model scalability, and prediction accuracy—are discussed, particularly in the context of data-poor environments, limiting broader model applicability. The paper concludes by outlining future directions, emphasizing context-specific AI implementations, the need for public–private collaboration, and policy interventions to enhance scalability and adoption in food security contexts.

99 GENERAL AND MISCELLANEOUS↗

Coupled machine learning–ecosystem ensemble models substantially improve predictions of nitrous oxide (N 2 O) fluxes from US croplands

Nitrous oxide (N 2 O) is a potent and persistent greenhouse gas, with rising atmospheric concentrations driven in part by inefficient use of synthetic nitrogen (N) fertilizers in agriculture. Predicting soil N 2 O emissions is challenging due to high spatial and temporal variability arising from complex soil biogeochemical processes. Process-based ecosystem models and standalone machine learning (ML) approaches without extensive site-specific calibration often miss high-emission episodes. Here, we show how an Ensemble Modeling System (EMS) based on outputs from an ensemble of ecosystem models coupled to an ensemble of ML models can improve predictions and understanding of N 2 O fluxes from US cropland. Trained and validated on ~12,000 N 2 O chamber measurements at 17 US Midwest sites (six crops, 35 management practices), the EMS accurately predicted daily fluxes of N 2 O at both training (R 2 = 0.84, RMSE = 16.4 g N ha −1 d −1 ) and held-out testing sites (R 2 = 0.84, RMSE = 6.2 g N ha −1 d −1 ). Analyses identified six dominant N 2 O drivers: soil organic carbon (SOC), NH 4 + , NO 3 - , water-filled pore space, temperature, and aboveground biomass production. Wet, warm soils produced large N 2 O peaks only with sufficient SOC and mineral N; in low-SOC soils, fluxes remained low. Incorporating these drivers into process-based models might significantly improve their predictive capacity. The EMS demonstrates a strong potential to predict N 2 O fluxes at unseen sites, enabling more reliable regional inventories, improved gap-filling where measurements are sparse, and enhanced understanding of mechanisms to advance targeted mitigation strategies in food, feed, and bioenergy crops.

AI↗

Machine learning for reparameterization of multi-scale closures

Scientific machine learning (ML) is becoming increasingly useful in learning closure models for multi-scale physics problems; however, many ML approaches require a vast array of training data and can struggle with generalization and interpretability. Here, rather than learning an entire closure operator, we adopt an existing reduced-dimension model of the microphysics and learn an optimal re-parameterization of the solver. We demonstrate two approaches for training the reduced dimension closure model (1) an a priori method that optimizes the closure parameterization and the neural network parameters separately and (2) an a posteriori method that simultaneously optimizes both. Using the simulation of biomass pyrolysis as a motivating example, we show that the a posteriori method achieves better target losses and is less dependent on training dataset size for generalizability. We then demonstrate the impact that implementing this reparameterization has at the macroscale, showing improved predictive performance with no modification to the underlying macroscale solvers.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗