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At least 811 records · Page 45

Control simulations of many-body quantum systems by a synergism of discrete real-time learning and optimal control theory

We present a self-consistent algorithm for optimal control simulations of many-body quantum systems. The algorithm features a two-step synergism that combines discrete real-time machine learning (DRTL) with Quantum Optimal Control Theory (QOCT) using the time-dependent Schrödinger equation. Specifically, in step (1), DRTL is employed to identify a compact working space (i.e., the important portion of the Hilbert space) for the time evolution of the many-body quantum system in the presence of a control field (i.e., the initial or previously updated field), and in step (2), QOCT utilizes the DRTL-determined working space to find a newly updated control field for a chosen objective. Steps 1 and 2 are iterated until a self-consistent control objective value is reached such that the resulting optimal control field yields the same targeted objective value when the corresponding working space is systematically enlarged. Furthermore, to demonstrate this two-step self-consistent DRTL-QOCT synergistic algorithm, we perform optimal control simulations of strongly interacting 1D as well as 2D Heisenberg spin systems. In both scenarios, only a single spin (at the left end site for 1D and the upper left corner site for 2D) is driven by the time-dependent control fields to create an excitation at the opposite site as the target. It is found that, starting from all spin-down zero excitation states, the synergistic method is able to identify working spaces and convergence of the desired controlled dynamics with just a few iterations of the overall algorithm. In the cases studied, the dimensionality of the working space scales only quasi-linearly with the number of spins.

Artificial neural networks↗

MOOSE ProbML: Parallelized probabilistic machine learning and uncertainty quantification for computational energy applications

Here, this paper presents the development and demonstration of massively parallel probabilistic machine learning (ML) and uncertainty quantification (UQ) capabilities within the Multiphysics Object-Oriented Simulation Environment (MOOSE), an open-source computational platform for parallel finite element and finite volume analyses. In addressing the computational expense and uncertainties inherent in complex multiphysics simulations, this paper integrates Gaussian process (GP) variants, active learning, Bayesian inverse UQ, adaptive forward UQ, Bayesian optimization, evolutionary optimization, and Markov chain Monte Carlo (MCMC) within MOOSE. It also elaborates on the interaction among key MOOSE systems — Sampler, MultiApp, Reporter, and Surrogate — in enabling these capabilities. The modularity offered by these systems enables development of a multitude of probabilistic ML and UQ algorithms in MOOSE. Example code demonstrations include parallel active learning and parallel Bayesian inference via active learning. The impact of these developments is illustrated through five applications relevant to computational energy applications: UQ of nuclear fuel fission product release, using parallel active learning Bayesian inference; very rare events analysis in nuclear microreactors using active learning; advanced manufacturing process modeling using multi-output GPs (MOGPs) and dimensionality reduction; fluid flow using deep GPs (DGPs); and tritium transport model parameter optimization for fusion energy, using batch Bayesian optimization. These capabilities are part of the MOOSE framework.

97 - MATHEMATICS AND COMPUTING↗

Controlling extrapolations of nuclear properties with feature selection

Predictions of nuclear properties far from measured data are inherently inaccurate because of uncertainties in our knowledge of nuclear forces and in our treatment of quantum many-body effects in strongly-interacting systems. While the model bias can be directly calculated when experimental data is available, only an estimate can be made in the absence of such measurements. Current approaches to compute the estimated bias quickly lose predictive power when their input variables are taken far from the training region, resulting in uncontrolled uncertainties in applications such as nucleosynthesis simulations. In this letter, we present a novel technique to identify the input variables of machine learning algorithms that can provide robust estimates of model bias. Our process is based on selecting input variables, or features, based on their probability distribution functions across the entire nuclear chart. We illustrate our approach on the problem of quantifying the model bias in nuclear binding energies calculated with Density Functional Theory (DFT). We prove that building model biases with only Z and N as features leads to highly unreliable extrapolations. Conversely, we show that proper feature selection can systematically improve theoretical predictions without increasing uncertainties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Disentangling the Impacts of Microtopography and Shrub Distribution on Snow Depth in a Subarctic Watershed: Toward a Predictive Understanding of Snow Spatial Variability

Snow plays a critical role in carbon cycling, vegetation dynamics, and permafrost hydrology at high latitudes by influencing surface energy exchange. Predicting snow distribution patterns is essential for understanding the evolution of Arctic ecosystems, yet scaling process-level knowledge to landscape predictions remains challenging. Here, we analyze snow depth (2019 and 2022), terrain elevation, and vegetation height from a watershed on the Seward Peninsula, Alaska, to examine how topography and shrubs shape snow redistribution across spatial scales. We find that snow depth is strongly coupled to terrain at scales below ∼60 m but becomes increasingly decoupled at larger scales. The topographic model of snow depth variation, which transforms terrain data to align with these scale-dependent snow patterns, is well correlated with local snow depth variations (linear fit R 2 > 0.5 for 85% of 100-m patches). A machine learning reconstruction of shrub canopy snow trapping reveals a simple exponential relationship between canopy structure and snow accumulation ( R 2 = 0.59), highlighting the combined influence of topography and vegetation on snow distribution. Together, these empirical relationships capture much of the observed snow variability in the watershed ( R 2 = 0.49, root mean square error (RMSE) = 30 cm), though systematic limitations persist in areas of strong scour and at coarser scales where wind-terrain interactions are more complex. These findings provide a framework for more efficient snow depth prediction and offer insights to improve snow-vegetation feedback representation in Earth System Models.

54 ENVIRONMENTAL SCIENCES↗

Structure of chalcogen overlayers on Au(111): Density functional theory and lattice-gas modeling

Ordering of different chalcogens, S, Se, and Te, on Au(111) exhibit broad similarities but also some distinct features, which must reflect subtle differences in relative values of the long-range pair and many-body lateral interactions between adatoms. We develop lattice-gas (LG) models within a cluster expansion framework, which includes about 50 interaction parameters. These LG models are developed based on density functional theory (DFT) analysis of the energetics of key adlayer configurations in combination with the Monte Carlo (MC) simulation of the LG models to identify statistically relevant adlayer motifs, i.e., model development is based entirely on theoretical considerations. The MC simulation guides additional DFT analysis and iterative model refinement. Given their complexity, development of optimal models is also aided by strategies from supervised machine learning. The model for S successfully captures ordering motifs over a broader range of coverage than achieved by previous models, and models for Se and Te capture the features of ordering, which are distinct from those for S. More specifically, the modeling for all three chalcogens successfully explains the linear adatom rows (also subtle differences between them) observed at low coverages of ~0.1 monolayer. The model for S also leads to a new possible explanation for the experimentally observed phase with a (5 × 5)-type low energy electron diffraction (LEED) pattern at 0.28 ML and to predictions for LEED patterns that would be observed with Se and Te at this coverage.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

matsim-agents v1.0

matsim-agents is a multi-agent AI framework for atomistic materials simulation and discovery. It orchestrates large language models (LLMs), machine-learned interatomic potentials (MLIPs), and DFT codes into a single agentic loop running on laptops and DOE leadership-class supercomputers. MULTI-AGENT ORCHESTRATION A LangGraph state machine with three nodes: a Planner that converts a natural-language research objective into structured tasks; an Executor that dispatches atomistic tools and loops until the queue is empty; and an Analyst that summarizes results into a human-readable report. State is checkpointed after every step and human-in-the-loop gates can be inserted at any edge. HYPOTHESIS-DRIVEN DISCOVERY CHAT An interactive REPL (matsim-agents chat) that couples LLM dialogue with atomistic simulation. Chemical formulas are automatically detected in conversation turns and trigger a full crystal-phase exploration: structure generation → relaxation → stability scoring → result injection back into the conversation, creating a closed hypothesis-refinement loop. CRYSTAL PHASE ENUMERATION Given a composition, the phase explorer enumerates prototypes by stoichiometry: elemental (fcc/bcc/hcp/sc/diamond), binary 1:1 (rocksalt/CsCl/zincblende/ wurtzite/fluorite/rutile), ternary 1:1:3 (cubic perovskite), ternary 1:2:4 (perovskite + spinel), quaternary 1:1:2:6 (Fm-3m double perovskite). 2-D prototypes (graphene, h-BN, MoS2 2H/1T) and multilayer stacking are also supported via --include-2d and --num-layers. SUPERCELL GENERATION AND SITE DECORATION Auto-tiling to a minimum atom count (--min-atoms), explicit NxNxN tiling (--supercell), symmetry-distinct site decorations (--n-orderings), and isotropic lattice-scale sweeps (--lattice-scales) for volume bracketing. MLFF RELAXATION AND STABILITY SCORING HydraGNN (multi-headed GNN) drives structure relaxation via ASE with FIRE, BFGS, or BFGSLineSearch. Stability output: delta-E/atom ranking across phases and a max-residual-force dynamical-stability proxy. Other MLIPs (MACE, NequIP, Orb) can be plugged in through the same interface. DFT BACKENDS Quantum ESPRESSO pw.x and VASP 6.6 are first-class labellers. Both have validated GPU builds and SLURM/PBS launchers for three DOE platforms: Frontier (AMD MI250X, ROCm), Aurora (Intel PVC, oneAPI), Perlmutter (NVIDIA A100, CUDA). QE produces ~100 binaries (pw.x, ph.x, epw.x, ...). VASP supports scf, relax, vc-relax, and vc-relax-shape run types. ACTIVE-LEARNING LOOP matsim-agents al run CONFIG.yaml drives an iterative HydraGNN-DFT loop: MD generates candidates → ensemble/MC-dropout uncertainty selects the most informative → DFT labels them in parallel inside one allocation → dataset grows → HydraGNN retrains → repeat. DFT backend is a single YAML toggle (dft.backend: vasp | qe). LLM-generated seed structures are supported (no curated POSCAR library needed). Config uses ${VAR}, ${VAR:-default}, ${VAR:?msg} shell-style substitution for cross-user/cross-site portability. LLM BACKENDS Ollama (local, default), vLLM (HPC multi-GPU serving), OpenAI, Anthropic, HuggingFace Transformers+Accelerate. Selected at runtime via flag or env var with no code changes. HPC PORTABILITY Same Python entry points run on Frontier (ROCm 7.2), Aurora (oneAPI), and Perlmutter (CUDA 12). DFT and ML stacks are never co-loaded in the same shell; they couple through the scheduler and filesystem. Advanced multi-node launchers (serve, discovery-chat, single-relaxation, active-learning, QE warm-start) are provided for all three platforms. CODABENCH COMPETITION BUNDLE A self-contained benchmark: 159 atomistic test structures across 11 material classes, 5 tasks (formation energy, forces, ML relaxation, AI-DFT relaxation, phase stability ranking), public/private leaderboard split (30/70), and four ready-to-run baselines: MACE-MP-0, HydraGNN, UMA, AllScAIP.

Lupo Pasini, Massimiliano [Oak Ridge National Labo↗

Accelerating laser ray tracing in high fidelity physics simulations of laser melting using squeeze U-net

Laser melting is a core component of the ongoing industrial revolution, dubbed Industry 4.0, as lasers facilitate fast and precise melting and fusion in advanced manufacturing. There is a strong need to optimize the laser process using simulations. However, this has proven challenging as high fidelity simulations are needed for predictive modeling and this is currently prohibitively expensive even when run on hundreds of processors on high performance computers. The challenge is capturing complex physics of laser material interaction, fluid dynamics, thermal physics and material phase transformations at various length and time scales. To close this technological gap, we modified a squeeze U-net to accelerate the laser ray tracing component of such high fidelity models by ~4x–40x while preserving the core physics principle of conservation of energy with 97% accuracy. This approach enables the accurate modeling of global laser energy absorption as a function of local surface temperatures and complex surface topologies, which govern the reflection directions and energy losses of laser rays upon interacting with the material surface.

Computer science↗

Advances and perspectives in discovery and functional analysis of small secreted proteins in plants

Small secreted proteins (SSPs) are less than 250 amino acids in length and are actively transported out of cells through conventional protein secretion pathways or unconventional protein secretion pathways. In plants, SSPs have been found to play important roles in various processes, including plant growth and development, plant response to abiotic and biotic stresses, and beneficial plant–microbe interactions. Over the past 10 years, substantial progress has been made in the identification and functional characterization of SSPs in several plant species relevant to agriculture, bioenergy, and horticulture. Yet, there are potentially a lot of SSPs that have not been discovered in plant genomes, which is largely due to limitations of existing computational algorithms. Recent advances in genomics, transcriptomics, and proteomics research, as well as the development of new computational algorithms based on machine learning, provide unprecedented capabilities for genome-wide discovery of novel SSPs in plants. In this review, we summarize known SSPs and their functions in various plant species. Then we provide an update on the computational and experimental approaches that can be used to discover new SSPs. Finally, we discuss strategies for elucidating the biological functions of SSPs in plants.

59 BASIC BIOLOGICAL SCIENCES↗

Enabling robust offline active learning for machine learning potentials using simple physics-based priors

Abstract Machine learning surrogate models for quantum mechanical simulations have enabled the field to efficiently and accurately study material and molecular systems. Developed models typically rely on a substantial amount of data to make reliable predictions of the potential energy landscape or careful active learning (AL) and uncertainty estimates. When starting with small datasets, convergence of AL approaches is a major outstanding challenge which has limited most demonstrations to online AL. In this work we demonstrate a Δ-machine learning (ML) approach that enables stable convergence in offline AL strategies by avoiding unphysical configurations with initial datasets as little as a single data point. We demonstrate our framework’s capabilities on a structural relaxation, transition state calculation, and molecular dynamics simulation, with the number of first principle calculations being cut down anywhere from 70%–90%. The approach is incorporated and developed alongside AMP torch , an open-source ML potential package, along with interactive Google Colab notebook examples.

Shuaibi, Muhammed↗

Dynamic Networks Experiment FY18 - Quality Control Focus Area Efforts

The availability of data whose quality is fittingly labeled is of tantamount importance to signal detection and all other downstream signal processing operations. Without identification, the goals of low yield nuclear monitoring cannot reach their full potential. A fundamental question that remains is the knowledge of the capability gaps that prevent us from using open network data. With these new channels, we will need better understanding of the frequency, type, severity, and impact of artifacts when compared to conventional networks. Moreover, beyond a simple quality label, thresholds for acceptable use of the data will need to be established, likely on a use case by use case basis. Finally, orders of magnitude more data with an at-best static analyst pool size means that quality artifacts must be identified with as little human interaction as possible. Automated methodologies must be developed to account for the scale of the problem when ad hoc networks are candidates for processing. At the same time that “data wealth” provides more opportunity for signal exploitation, the introduction of ad hoc networks introduces an increased risk quality issues in both sensor value and metadata issues. The artifacts shown below are examples of some sensor-based quality issues that impair downstream processing. The machine learning model used in this project was able to identify the artifacts that produce these spurious correlations, significantly improving analyst productivity.

97 MATHEMATICS AND COMPUTING↗

Development of an interatomic potential for the Ta–Li system

A new interatomic potential for the Ta–Li system is introduced to facilitate the study of phase stability, mechanical properties and non-equilibrium dynamics after Li implantation in Ta. Here, this potential is based on a generalization of the embedded atom method (GEAM) and includes contributions from embedding energy, explicit two- and three-body interactions, and nonlocal many-body interaction terms. The parameters of the potential are optimized using energies and atomic forces for a wide range of configurations obtained from ab initio density functional theory (DFT) calculations. The potential is rigorously validated across a range of physical properties, including elastic constants, equations of state, phonon dispersion curves, point defect properties, and melting temperatures for different compositions. Although our potential is trained on a small dataset, its accuracy is comparable to that of available machine learning potentials for Li and Ta. Our simulations show that at temperatures below 500 K, Li atoms in Ta–Li alloys form clusters separated by Ta-rich domains, and we find no evidence of ordered phase formation. For Li concentrations below a few percent, Li atoms preferentially segregate to surfaces and grain boundaries. However, in alloys containing more than ~10% Li, the accumulation of Li in symmetric-tilt grain boundaries can lead to one of the following effects: formation of amorphous-like regions, changes in grain boundary structural units, or lateral movement of the grain boundary.

GEAM potential↗

Enabling reactive microscopy with MicroMator

Microscopy image analysis has recently made enormous progress both in terms of accuracy and speed thanks to machine learning methods and improved computational resources. This greatly facilitates the online adaptation of microscopy experimental plans using real-time information of the observed systems and their environments. Applications in which reactiveness is needed are multifarious. Here we report MicroMator, an open and flexible software for defining and driving reactive microscopy experiments. It provides a Python software environment and an extensible set of modules that greatly facilitate the definition of events with triggers and effects interacting with the experiment. We provide a pedagogic example performing dynamic adaptation of fluorescence illumination on bacteria, and demonstrate MicroMator’s potential via two challenging case studies in yeast to single-cell control and single-cell recombination, both requiring real-time tracking and light targeting at the single-cell level.

47 OTHER INSTRUMENTATION↗

Inference offers a metric to constrain dynamical models of neutrino flavor transformation

The multimessenger astrophysics of compact objects presents a vast range of environments where neutrino flavor transformation may occur and may be important for nucleosynthesis, dynamics, and a detected neutrino signal. Development of efficient techniques for surveying flavor evolution solution spaces in these diverse environments, which augment and complement existing sophisticated computational tools, could leverage progress in this field. To this end we continue our exploration of statistical data assimilation (SDA) to identify solutions to a small-scale model of neutrino flavor transformation. SDA is a machine learning formula wherein a dynamical model is assumed to generate any measured quantities. Specifically, we use an optimization formulation of SDA wherein a cost function is extremized via the variational method. Regions of state space in which the extremization identifies the global minimum of the cost function will correspond to parameter regimes in which a model solution can exist. Our example study seeks to infer the flavor transformation histories of two monoenergetic neutrino beams coherently interacting with each other and with a matter background. We require that the solution be consistent with measured neutrino flavor fluxes at the point of detection, and with constraints placed upon the flavor content at various locations along their trajectories, such as the point of emission, and the locations of the Mikheyev-Smirnov-Wolfenstein resonances. We show how the procedure efficiently identifies solution regimes and rules out regimes where solutions are infeasible. Overall, results in this work intimate the promise of this “variational annealing” methodology to efficiently probe an array of fundamental questions that traditional numerical simulation codes render difficult to access.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Estimating soybean yields from high-temporal-resolution multi-source data using deep learning

Accurate and timely crop yield prediction is crucial for ensuring food security and maintaining stable agricultural markets. In recent years, there has been a surge in interest in leveraging high-temporal-resolution, multi-source data for effective crop growth monitoring and yield estimation. A notable challenge arises from the difficulty in capturing the intricate interactions between variables across different time steps within these high-temporal-resolution time series datasets. This complexity hinders the reliable extraction of yield information from voluminous and often noisy datasets, especially during periods of extreme weather events. Here, in this study, we propose an Attention and Graph Isomorphism Network-enhanced Bi-directional Long Short-Term Memory network (AGB-LSTM) for estimating county-level soybean yield in the United States. This model integrates a diverse set of remote sensing data, including Near-Infrared Reflectance of Vegetation (NIRv), Sun-Induced chlorophyll Fluorescence (SIF), and Gross Primary Productivity (GPP), along with environmental covariates. The AGB-LSTM effectively leverages information related to crop yield from high-temporal-resolution time series data (5-days), achieving an accuracy of R²= 0.67 and rRMSE = 14.46%. This approach significantly outperforms traditional machine learning methods such as Random Forest (RF) (R²= 0.52, rRMSE = 17.36%) and Bi-LSTM (R²= 0.58, rRMSE = 16.17%). Sensitivity experiments with different time steps and ranges demonstrated that our model could accurately and stably predict yields 1 to 2 months before harvest. Moreover, data with a finer temporal resolution consistently improved prediction performance, resulting in an approximately 20% increase in and an approximately 20% decrease in rRMSE compared to using monthly composites. We also evaluated the robustness of the model under extreme climate events and observed strong performance (R²= 0.50, rRMSE = 21.32%). Finally, yield mapping for major soybean-producing regions in North America in 2023 revealed spatial patterns that closely matched USDA yield reports. Our findings suggest that the AGB-LSTM model is a promising and effective method for estimating yield and has notable potential for global crop yield forecasting.

Deep learning↗

Detecting Masquerade Attacks in Controller Area Networks Using Graph Machine Learning

Modern vehicles rely on a myriad of electronic control units (ECUs) interconnected via controller area networks (CANs) for critical operations. Despite their ubiquitous use and reliability, CANs are susceptible to sophisticated cyberattacks, particularly masquerade attacks, which inject false data that mimic legitimate messages at the expected frequency. These attacks pose severe risks such as unintended acceleration, brake deactivation, and rogue steering. Traditional intrusion detection systems (IDS) often struggle to detect these subtle intrusions due to their seamless integration into normal traffic. This paper introduces a novel framework for detecting masquerade attacks in the CAN bus using graph machine learning (ML). We hypothesize that the integration of shallow graph embeddings with time series features derived from CAN frames enhances the detection of masquerade attacks. We show that by representing CAN bus frames as message sequence graphs (MSGs) and enriching each node with contextual statistical attributes from time series, we can enhance detection capabilities across various attack patterns compared to using graph-based features only. Our method ensures a comprehensive and dynamic analysis of CAN frame interactions, improving robustness and efficiency. Extensive experiments on the ROAD dataset validate the effectiveness of our approach, demonstrating statistically significant improvements in the detection rates of masquerade attacks compared to a baseline that uses graph-based features only as confirmed by Mann-Whitney U and Kolmogorov-Smirnov tests (p < 0.05) .

Marfo, William [Univ. of Texas, El Paso, TX (Unite↗

Position Papers for Inverse Methods for Complex Systems under Uncertainty Workshop

The ability to solve inverse problems – inferring unknown parameters, structures, or states of a system from observed data – is essential for advancing scientific discovery and innovation capabilities for the DOE mission. Basic research needs and challenges are particularly acute in emerging areas such as the interactive, data-driven, modeling and simulation of digital twins; decision support for experiments at DOE scientific user facilities; and for other complex systems and workflows. Inverse problems are at the heart of understanding and controlling complex systems due to factors such as observational data with varying modalities and fidelities, inherent uncertainties in physical measurements and numerical models, and the computational demands of rapid and high-fidelity simulations. The convergence of recent scientific computing trends – scientific machine learning, artificial intelligence, and computing advances such as exascale computing – is creating unprecedented opportunities. These advancements offer the potential to revolutionize how we approach inverse problems to extract actionable insights with the required level of accuracy and computational efficiency. This workshop and the Call for Position Papers are vital steps in bringing together experts to collectively explore and identify the new computational and mathematical directions needed in inverse methods for complex systems under uncertainty.

97 MATHEMATICS AND COMPUTING↗

Updates to the Alliance of Genome Resources central infrastructure

The Alliance of Genome Resources (Alliance) is an extensible coalition of knowledgebases focused on the genetics and genomics of intensively studied model organisms. The Alliance is organized as individual knowledge centers with strong connections to their research communities and a centralized software infrastructure, discussed here. Model organisms currently represented in the Alliance are budding yeast, Caenorhabditis elegans, Drosophila, zebrafish, frog, laboratory mouse, laboratory rat, and the Gene Ontology Consortium. The project is in a rapid development phase to harmonize knowledge, store it, analyze it, and present it to the community through a web portal, direct downloads, and application programming interfaces (APIs). Here, we focus on developments over the last 2 years. Specifically, we added and enhanced tools for browsing the genome (JBrowse), downloading sequences, mining complex data (AllianceMine), visualizing pathways, full-text searching of the literature (Textpresso), and sequence similarity searching (SequenceServer). We enhanced existing interactive data tables and added an interactive table of paralogs to complement our representation of orthology. To support individual model organism communities, we implemented species-specific “landing pages” and will add disease-specific portals soon; in addition, we support a common community forum implemented in Discourse software. We describe our progress toward a central persistent database to support curation, the data modeling that underpins harmonization, and progress toward a state-of-the-art literature curation system with integrated artificial intelligence and machine learning (AI/ML).

59 BASIC BIOLOGICAL SCIENCES↗

Classical analog of quantum models in synthetic dimensions

We introduce a classical analog of quantum matter in ultracold molecule-synthetic or Rydberg atom-synthetic dimensions, by extending the Potts model to include interactions J 1 between atoms adjacent in both real and synthetic space and studying its finite-temperature properties. For intermediate values of J 1 , the resulting phases and phase diagrams are similar to those of the clock and Villain models, in which three phases emerge. There exists a sheet phase analogous to that found in quantum synthetic dimension models between the high-temperature disordered phase and the low-temperature ferromagnetic phase. Furthermore, we also employ machine learning to uncover nontrivial features of the phase diagram using the learning by confusion approach, which is able to discern several successive phase transitions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗