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At least 1,783 records · Page 99

Enhancing Electron Microscopy Image Classification Using Data Augmentation

Manual labeling for machine learning tasks such as image classification is tedious and labor-intensive; as a result, scientific datasets suitable for deep learning applications are scarce and limited. While data augmentation techniques have shown promise for extending image datasets, very little work has been done to understand the impact of combining multiple augmentation methods sequentially or the limits of their effectiveness when combined. Our work addresses this gap by examining how standard and combinatorial data augmentation affects the performance of machine learning models when trained on small datasets for label classification tasks. For our analysis, we generate single, double and quadruple-augmented datasets for a microscopy image classification task using six standard augmentation methods, and compare the resultant improvements observed in binary classification accuracy with three standard image classification models (DenseNet169, MobileNetV2, ResNet101V2). Our experiments show a non-monotonic relationship between the number of simultaneous augmentation methods and classification accuracy, indicating that there is a trade-off between the degree of augmentation and the model performance. These findings suggest that the optimal number of augmentation methods will vary by domain and use case. We also find that the order in which augmentation methods are applied to a limited dataset matters when combining augmentation schemes, with our use case showing performance differences up to 2.6% when the augmentation order is reversed for double-augmented datasets. Our work offers insights to the limits of data augmentation when working on image classification tasks with limited datasets.

Welsman, Jordan A↗

Strangers in a foreign land: ‘Yeastizing’ plant enzymes

Abstract Expressing plant metabolic pathways in microbial platforms is an efficient, cost‐effective solution for producing many desired plant compounds. As eukaryotic organisms, yeasts are often the preferred platform. However, expression of plant enzymes in a yeast frequently leads to failure because the enzymes are poorly adapted to the foreign yeast cellular environment. Here, we first summarize the current engineering approaches for optimizing performance of plant enzymes in yeast. A critical limitation of these approaches is that they are labour‐intensive and must be customized for each individual enzyme, which significantly hinders the establishment of plant pathways in cellular factories. In response to this challenge, we propose the development of a cost‐effective computational pipeline to redesign plant enzymes for better adaptation to the yeast cellular milieu. This proposition is underpinned by compelling evidence that plant and yeast enzymes exhibit distinct sequence features that are generalizable across enzyme families. Consequently, we introduce a data‐driven machine learning framework designed to extract ‘yeastizing’ rules from natural protein sequence variations, which can be broadly applied to all enzymes. Additionally, we discuss the potential to integrate the machine learning model into a full design‐build‐test cycle.

59 BASIC BIOLOGICAL SCIENCES↗

Computational Tools and Workflows for Quantitative Risk Assessment and Decision Support for Geologic Carbon Storage Sites: Progress and Insights from the U.S. DOE’s National Risk Assessment Partnership

The 2005 Intergovernmental Panel on Climate Change (IPCC) Special Report on CCS raised the profile of CO2 capture and storage (CCS) as an important technology for reducing greenhouse gas (GHG) emissions. CCS is now recognized as a key component of most climate change mitigation scenarios. Since publication of that report the international research, development, and deployment (RD&D) community has advanced key technical aspects, clarified regulatory requirements, explored value chain and infrastructure solutions, and developed incentive paradigms to enable and promote large-scale deployment of CCS. These efforts have included research to better characterize geologic storage resources, to improve injection performance and storage efficiency, to assess and manage subsurface environmental risks, and to advance monitoring technologies to assure system conformance. These efforts have helped to build confidence in the viability of geologic carbon storage (GCS), but stakeholder concerns about long-term risks and liability associated with GCS remain a hurdle to broad acceptance and large-scale deployment of CCS. Since 2010, the U.S. DOE’s National Risk Assessment Partnership (NRAP) – a research collaboration between five contributing national laboratories – has worked to establish and demonstrate methods and tools to quantify and manage the subsurface environmental risks associated with GCS, amidst uncertainty. This work supports the Office of Fossil Energy and Carbon Management Carbon Transport and Storage Program’s goal of advancing safe and secure commercial-scale GCS deployment. To address the technical challenge of simulating the physical response of the GCS site to large-scale CO2 injection, NRAP has adopted an approach that relies on coupling computationally efficient reduced-order and/or data-driven proxy models of important system components (i.e., storage reservoir, sealing caprock, leakage pathways, intermediate formations, overlying groundwater aquifers, and the atmosphere) in integrated assessment framework. That integrated model of the physical system is complemented with fit-for purpose functionality to support site characterization and risk-related decisions. The recently released NRAP Phase II toolset includes the Open-Source Integrated Assessment Model (NRAP-Open-IAM) for evaluation of trends in leakage risk and potential impact, tools to support monitoring design optimization (Designs for Risk Evaluation and Management – DREAM v3.0 and Passive Seismic Monitoring Tool - PSMT), and tools for state of stress evaluation (State-of-Stress Analysis Tool - SOSAT) and forecasting induced seismicity risk. The NRAP team has also released a pair of reports describing conceptual workflows to incorporate physics-based, quantitative risk assessment into many of the design, planning, operation, and closure decisions for GCS projects. An online catalogue highlights published studies where these tools and methods are demonstrated. In this presentation, the utility of these products to assess risks and address key stakeholder questions will be highlighted through examples, and related insights about the safety and security of geologic carbon storage in qualified storage sites will be discussed. The prospect of rapid, large-scale deployment of GCS technology to aggressively reduce anthropogenic CO2 emissions requires careful consideration of interference between multiple commercial-scale storage projects within a basin. Going forward, NRAP is expanding and adapting site-scale risk quantification tools and methods to enable assessment of risks and inform management decisions for basin-scale deployment. Increasingly, this work will leverage next-generation approaches for surrogate modelling, fast prediction, and advanced visualization enabled by machine learning and artificial intelligence to promote virtual learning, scenario evaluation, and augment risk-based decision making.

quantitative risk assessment, geologic carbon stor↗

DiffLense: a conditional diffusion model for super-resolution of gravitational lensing data

Abstract Gravitational lensing data is frequently collected at low resolution due to instrumental limitations and observing conditions. Machine learning-based super-resolution techniques offer a method to enhance the resolution of these images, enabling more precise measurements of lensing effects and a better understanding of the matter distribution in the lensing system. This enhancement can significantly improve our knowledge of the distribution of mass within the lensing galaxy and its environment, as well as the properties of the background source being lensed. Traditional super-resolution techniques typically learn a mapping function from lower-resolution to higher-resolution samples. However, these methods are often constrained by their dependence on optimizing a fixed distance function, which can result in the loss of intricate details crucial for astrophysical analysis. In this work, we introduce DiffLense , a novel super-resolution pipeline based on a conditional diffusion model specifically designed to enhance the resolution of gravitational lensing images obtained from the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP). Our approach adopts a generative model, leveraging the detailed structural information present in Hubble space telescope (HST) counterparts. The diffusion model, trained to generate HST data, is conditioned on HSC data pre-processed with denoising techniques and thresholding to significantly reduce noise and background interference. This process leads to a more distinct and less overlapping conditional distribution during the model’s training phase. We demonstrate that DiffLense outperforms existing state-of-the-art single-image super-resolution techniques, particularly in retaining the fine details necessary for astrophysical analyses.

Computer Science↗

Data efficiency and extrapolation trends in neural network interatomic potentials

Abstract Recently, key architectural advances have been proposed for neural network interatomic potentials (NNIPs), such as incorporating message-passing networks, equivariance, or many-body expansion terms. Although modern NNIP models exhibit small differences in test accuracy, this metric is still considered the main target when developing new NNIP architectures. In this work, we show how architectural and optimization choices influence the generalization of NNIPs, revealing trends in molecular dynamics (MD) stability, data efficiency, and loss landscapes. Using the 3BPA dataset, we uncover trends in NNIP errors and robustness to noise, showing these metrics are insufficient to predict MD stability in the high-accuracy regime. With a large-scale study on NequIP, MACE, and their optimizers, we show that our metric of loss entropy predicts out-of-distribution error and data efficiency despite being computed only on the training set. This work provides a deep learning justification for probing extrapolation and can inform the development of next-generation NNIPs.

36 MATERIALS SCIENCE↗

Highly-scalable, physics-informed GANs for learning solutions of stochastic PDEs

Uncertainty quantification for forward and inverse problems is a central challenge across physical and biomedical disciplines. We address this challenge for the problem of modeling subsurface flow at the Hanford Site by combining stochastic computational models with observational data using physics-informed GAN models. The geographic extent, spatial heterogeneity, and multiple correlation length scales of the Hanford Site require training a computationally intensive GAN model to thousands of dimensions. We develop a highly optimized implementation that scales to {\herogpucount} NVIDIA Volta GPUs. We develop a hierarchical scheme based on a multi-player game-theoretic approach for exploiting domain parallelism, map discriminators and generators to multiple GPUs, and employ efficient communication schemes to ensure training stability and convergence. Our implementation scales to {\heronodecount} nodes on the Summit supercomputer with a \weakscalingeff\% scaling efficiency, achieving peak and sustained half-precision rates of {\heropeakperf} PF/s and {\herosustainedperf} PF/s.

physics informed ML, machine learning, generative ↗

Multivariate Machine Learning Models of Nanoscale Porosity from Ultrafast NMR Relaxometry

Abstract Nanoporous materials are of great interest in many applications, such as catalysis, separation, and energy storage. The performance of these materials is closely related to their pore sizes, which are inefficient to determine through the conventional measurement of gas adsorption isotherms. Nuclear magnetic resonance (NMR) relaxometry has emerged as a technique highly sensitive to porosity in such materials. Nonetheless, streamlined methods to estimate pore size from NMR relaxometry remain elusive. Previous attempts have been hindered by inverting a time domain signal to relaxation rate distribution, and dealing with resulting parameters that vary in number, location, and magnitude. Here we invoke well‐established machine learning techniques to directly correlate time domain signals to BET surface areas for a set of metal‐organic frameworks (MOFs) imbibed with solvent at varied concentrations. We employ this series of MOFs to establish a correlation between NMR signal and surface area via partial least squares (PLS), following screening with principal component analysis, and apply the PLS model to predict surface area of various nanoporous materials. This approach offers a high‐throughput, non‐destructive way to assess porosity in c.a. one minute. We anticipate this work will contribute to the development of new materials with optimized pore sizes for various applications.

Fricke, Sophia N.↗

Mesoscale Modeling to Characterize Eagle Soaring Habitat

Uncovering drivers of risk is crucial to understanding interactions between wildlife and wind turbines, and identifying options for impact minimization. These drivers tie to co-variates linked to behavior and movement patterns that allow us to estimate locations and periods of risk. For volant species, atmospheric flow can have significant influence on flight patterns. For obligate soaring birds, like golden eagles, updraft velocities can inform where eagles are likely to travel, at what altitude, and where conditions are not likely sufficient to sustain soaring flight. This has been an active area of study in recent years, using relatively coarse atmospheric data generally at the 20km x 20km scale or larger. Leveraging a 20-year dataset from the Weather Research and Forecasting Model (WRF) (https://www.mmm.ucar.edu/weather-research-and-forecasting-model), we are quantifying vertical velocities across the continental United States at a 2km x 2km resolution. Wind resource data sets originally were static maps showing the mean annual wind speed over an area. However, for these data sets to be optimally used for various applications they must be high-resolution time series, seamlessly span large geographic contexts, and account for uncertainty in wind speed. The National Renewable Energy Laboratory is producing public available datasets that meet these criteria and will be bias corrected to yield the most accurate wind resource data. This effort is an augment to the current WIND Toolkit which houses a high resolution data set. In the new iteration of the WIND Toolkit, a 20-year dataset will be used to improve the accuracy and estimate uncertainty using ensemble and machine-learning techniques. The resulting product will be the most accurate dataset of its size and at a 2km x 2km spatial and 5-minute temporal resolution. Through this work, a mesoscale vertical velocity layer will be produced by calculating the likelihood of orographic updraft and thermal updraft conditions across the continental United States. Specifically, we will use WRF model output combined with digital elevation maps to predict updrafts and then determine if vertical velocities are sufficient to support Golden Eagle soaring and gliding. Ultimately this data layer will be made available as a GIS layer in the Wind Prospector (maps.nrel.gov/wind-prospector/) tool or a similar framework. Data that will be incorporated include wind speed, direction temperature, relative humidity, barometric pressure, air density, precipitation rate, solar radiation, atmospheric stability, skin temperature, and upward heat flux. These products will advance research on interactions between volant species and wind energy by providing open access to highly resolved data with uncertainty quantification not previously available at this scale.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Physically Interpretable Neural Networks for the Geosciences: Applications to Earth System Variability

Abstract Neural networks have become increasingly prevalent within the geosciences, although a common limitation of their usage has been a lack of methods to interpret what the networks learn and how they make decisions. As such, neural networks have often been used within the geosciences to most accurately identify a desired output given a set of inputs, with the interpretation of what the network learns used as a secondary metric to ensure the network is making the right decision for the right reason. Neural network interpretation techniques have become more advanced in recent years, however, and we therefore propose that the ultimate objective of using a neural network can also be the interpretation of what the network has learned rather than the output itself. We show that the interpretation of neural networks can enable the discovery of scientifically meaningful connections within geoscientific data. In particular, we use two methods for neural network interpretation called backward optimization and layerwise relevance propagation, both of which project the decision pathways of a network back onto the original input dimensions. To the best of our knowledge, LRP has not yet been applied to geoscientific research, and we believe it has great potential in this area. We show how these interpretation techniques can be used to reliably infer scientifically meaningful information from neural networks by applying them to common climate patterns. These results suggest that combining interpretable neural networks with novel scientific hypotheses will open the door to many new avenues in neural network‐related geoscience research.

58 GEOSCIENCES↗

Modeling Single-Crystal Battery Materials: From Fundamental Understanding to Performance Evaluation

The performance of rechargeable batteries is fundamentally influenced by the physicochemical properties and microstructural features of their key material components. Recent experimental advancements have highlighted the potential of single-crystal (SC) morphologies to address inherent limitations of polycrystalline (PC) electrodes and solid-state electrolytes, offering tunable charge transport kinetics and improved cell cycling performance. Here, this review examines how state-of-the-art computational modeling, from atomistic and mesoscale to continuum-level approaches, including machine learning methodologies, has been utilized to investigate the critical factors governing the electrochemical behavior of SC battery materials. We explore how predictive modeling can elucidate the processing–structure–property–performance relationships of SC cathodes, anodes, and solid-state electrolytes, with a focus on unique SC characteristics such as crystallographic anisotropy, size effects, and facet-dependent properties. Additionally, we identify limitations in commonly used modeling techniques and discuss strategies to address these challenges. By integrating high-fidelity simulations with experimental insights, this review aims to outline a clear path for the rational design and optimization of SC battery components, paving the way for accelerated advancements in energy storage technologies.

Materials science↗

Online LIBS–ML Framework for Dynamic Characterization of Heterogeneous Waste-Derived Gasification Feedstocks

LIBS−ML framework for real time feedstock characterization during continuous conveyor transport Heterogeneous waste derived feedstocks (e.g., waste coal, biomass and blends) introduce rapid variability in heating value and ash chemistry that affect gasifier operation, yet conventional laboratory characterization techniques are too slow to support proactive control. To address this gap, this study reports on an online, in situ, dynamic characterization framework that couple’s laser-induced breakdown spectroscopy (LIBS) with leakage safe machine learning (ML) regression to deliver real time, decision quality predictions of gasifier relevant properties. A controlled sample matrix spanning two different waste coals, two different biomasses, and engineered blends under two particle size conditions were constructed and benchmarked using standardized laboratory analyses for proximate/ultimate properties and ash composition. LIBS spectra were acquired dynamically as material flowed on a conveyor belt, using high energy 1064 nm laser ablation and shot averaging to improve repeatability and precision. Supervised regression models (multi layer perceptron (MLP) /artificial neural network (ANN), random forest (RF), and support vector regression (SVR)) and an optimized weighted ensemble were trained on emission line feature sets using nested cross validation with Bayesian hyperparameter tuning and validated against an independent hold out set. The proposed LIBS−ML workflow achieves near laboratory predictive fidelity across parametric targets (including higher heating value (HHV), ash content, fixed carbon, sulfur, major ash forming oxides, and initial deformation temperature (IDT)), with the weighted ensemble providing a robust default predictor under dynamic measurement conditions. These results demonstrate a practical pathway for real time feedstock characterization that can enable feedforward adjustments and more resilient gasifier operation for variable quality waste derived fuels.

Biomass↗

Key Learnings from Hydraulic Fracturing Test Site - 2 (HFTS-2), Delaware Basin

Hydraulic fractures (HF) play a dominant role in oil and gas production from unconventional reservoirs, fracture characteristics, geometry, and extent are generally not well known and are typically inferred from various monitoring methods or subsurface models. The Hydraulic Fracturing Test Site-2 (HFTS-2) is a field-based research experiment performed in the Wolfcamp formation of the Permian (Delaware) Basin. HFTS-2, a unique joint industry program (JIP) that brings together government, academia, and industry, focused on field data acquisition and interpretation. The project has built a comprehensive HF research dataset that includes microseismic (MS), 1,500 ft of core, diagnostic formation injection tests (DFIT), fluid characterization, advanced logs, geochemistry, downhole gauges, varying completions, and permanent fiber optic (FO) cable in vertical and horizontal wells. These data were integrated and used to characterize HF geometry/dimensions and resulting depletion profiles, gain insights for completion design, and achieve a better understanding of parent well depletion effects on child well performance. The analysis and integration of the comprehensive HFTS-2 diagnostics dataset provide insights for optimal well placement and completions and improves understanding about the effects of parent well depletion. Furthermore, this dataset can be used to blind test and develop subsurface workflows for unconventional resources. Key learnings from HFTS-2 and the new technologies tested can easily be transferred to other unconventional plays.

58 GEOSCIENCES↗

HGQ: High Granularity Quantization for Real-time Neural Networks on FPGAs

Neural networks with sub-microsecond inference latency are required by many critical applications. Targeting such applications deployed on FPGAs, we present High Granularity Quantization (HGQ), a quantization-aware training framework that optimizes parameter bit-widths through gradient descent. Unlike conventional methods, HGQ determines the optimal bit-width for each parameter independently, making it suitable for hardware platforms supporting heterogeneous arbitrary precision arithmetic. In our experiments, HGQ shows superior performance compared to existing network compression methods, achieving orders of magnitude reduction in resource consumption and latency while maintaining the accuracy on several benchmark tasks. These improvements enable the deployment of complex models previously infeasible due to resource or latency constraints. HGQ is open-source and is used for developing next-generation trigger systems at the CERN ATLAS and CMS experiments for particle physics, enabling the use of advanced machine learning models for real-time data selection with sub-microsecond latency.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Control of matrix converters using machine learning

A method of controlling a matrix converter system is provided. The method includes receiving an operating condition and consulting a trained Q-data structure for reward values associated with respective switching states of the switching matrix for an operating state that corresponds to the operating condition. The Q-data structure is trained using Q-learning to map a reward value predicted for respective switching states to respective discrete operating states. The method further includes sorting the reward values predicted for the respective switching states mapped to the operating state that corresponds to the operating condition, selecting a subset of the set of the mappings as a function of a result of sorting the reward values associated with the switching states of the operating state, evaluating each switching state included in the subset, and selecting an optimal switching state for the operating condition based on a result of evaluating the switching states of the subset.

Chamie, Mahmoud El↗

Using dorsal surface for individual identification of dairy calves through 3D deep learning algorithms

Advances in machine learning techniques have allowed the development of computer vision systems (CVS) that can accurately predict several phenotypes of interest for livestock operations. In this context, 3D images taken from a top-down view are particularly useful for estimating body condition score, growth development, and body biometrics in cattle. Frequently, such CVS rely on identification (ID) systems, such as electronic tags, as a way to match animal ID and the predicted phenotype. However, the same 3D images used to predict body weight and other animal biometrics could be adopted for animal recognition as well. Such alternative would optimize CVS to recognize animal ID and monitor growth development simultaneously while leveraging the same hardware infrastructure. Furthermore, this strategy could be used to recognize animals with similar color patterns. Nonetheless, growing animals are continuously changing body shape, which could limit its use as an invariant feature for pattern recognition. Thus, the objectives of this study were: (1) to compare algorithms for different 3D object representations to identify individual animals; and (2) to evaluate how short-term changes in body shape due to animal growth affect the predictive performance of these algorithms. For objective 1, the algorithms were trained (n = 4,558) and tested (n = 1,139) using images from 38 Holstein calves. For objective 2, we designed three different experiments using images (n = 2,347) from five Holstein calves taken over six weeks during their growing period, always training and testing on different weeks. Each experiment evaluated how changing a different parameter of the image capturing procedure affected the predictive ability of the trained algorithms. In the first experiment, we varied the total number of images per animal in the training set; in the second experiment, we varied the number of weeks while keeping a fixed number of images in the training set; and in the third experiment, we skipped weeks between images in the training and test sets. The F 1 score for objective (1) was up to 0.804 when testing with the last frames of each video, and up to 0.959 when using random frames for testing. For objective (2), the F 1 score was up to 0.947 for the first experiment when using 130 images per animal; up to 0.979 for the second experiment when using all five weeks; and up to 0.917 when not skipping weeks between training and testing. In conclusion, these results show that deep learning algorithms can be used to identify individual animals through their dorsal area 3D surfaces, and, from our experiments using calves in their growing period, that they are robust enough to account for changes in body shape and size, making them a promising tool for animal recognition during growth.

3D neural networks↗

What Makes Au Nanospheres Superior to Octahedral and Cubic Counterparts for the Deposition of a Pt Monolayer Shell?

This study demonstrates that Au nanospheres are advantageous over their octahedral and cubic counterparts as seeds in the synthesis of Au@Pt core−shell nanocrystals with a monolayer shell. In combination with experimental characterization, we show through training a machine-learned interatomic potential that the Au nanospheres exhibit a large fraction of lowcoordination atoms which are uniformly distributed over the surface. The corresponding high-index facets, including {211}, {311}, {331}, {210}, and {310}, on a spherical seed promote nucleation while greatly shortening the diffusion distance for adatoms. In addition, the high-index facets are instrumental in retaining the deposited Pt atoms on the outermost surface by retarding their inter-diffusional exchange with the underlying Au atoms. By switching from a monolayer made of pure Pt to those made of Pt−Au alloys, we can optimize both the activity and selectivity of the nanocrystals toward the two-electron oxygen reduction reaction for the electrochemical synthesis of H 2 O 2 . This method should be extendible to the fabrication of other core−shell nanocatalysts with desired monolayer shells for various catalytic reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Training data selection for event classification in a highly variable environment

A problem of interest for nuclear nonproliferation is monitoring activities at nuclear facilities, where proliferation events may only take place a few times and often under variable conditions. Machine learning has revolutionized data analytics by enabling the use of measurable signatures to generate predictive models of facility operations. However, traditional methods for training these models require large, reliable data sets with labeled observations, a challenge for nonproliferation. Highly variable conditions further complicate this as events from training data may have occurred in conditions quite different from the event of interest. Our hypothesis is that when events occur in a highly variable environment, careful training data selection for each test event could outperform the standard approach of using all available training data. We developed a method to optimize training data selection for the given test event and applied it to predicting the power level of the High Flux Isotope Reactor (HFIR) at Oak Ridge National Laboratory. In this study, the reactor startup exhibits variability between occurrences due to natural variability in environmental conditions and operational procedures. Using a combination of analysis techniques, a similitude assessment was performed on data collected from HFIR to isolate clusters that were optimal for training a predictive model. Concepts such as dynamic time warping and Jaccard similarity were used in conjunction with clustering analysis. In order to validate this approach, the model was trained on every combination of unique training events and the predictive performance was compared to the performance using a subset of the training data selected by isolated clusters found through the similitude assessment.

Iyer, A↗

Design of quantum optical experiments with logic artificial intelligence

Logic Artificial Intelligence (AI) is a subfield of AI where variables can take two defined arguments, True or False, and are arranged in clauses that follow the rules of formal logic. Several problems that span from physical systems to mathematical conjectures can be encoded into these clauses and solved by checking their satisfiability (SAT). In contrast to machine learning approaches where the results can be approximations or local minima, Logic AI delivers formal and mathematically exact solutions to those problems. In this work, we propose the use of logic AI for the design of optical quantum experiments. We show how to map into a SAT problem the experimental preparation of an arbitrary quantum state and propose a logic-based algorithm, called Klaus, to find an interpretable representation of the photonic setup that generates it. We compare the performance of Klaus with the state-of-the-art algorithm for this purpose based on continuous optimization. We also combine both logic and numeric strategies to find that the use of logic AI significantly improves the resolution of this problem, paving the path to developing more formal-based approaches in the context of quantum physics experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗