Variational methods have offered controllable and powerful tools for capturing many-body quantum physics for decades. The recent introduction of expressive neural network quantum states has enabled the accurate representation of a broad class of complex wavefunctions for many Hamiltonians of interest. We introduce a first-principles method for building neural network representations of many-body excited states by adiabatically continuing eigenstates of simple Hamiltonians into the strongly correlated regime. With controlled access to the full many-body gap, we obtain accurate estimates of critical exponents. Successive eigenstate estimates can be run entirely in parallel, enabling precise targeting of excited-state properties without reference to the rest of the spectrum, opening the door to large-scale numerical investigations of universal properties of entire phases of matter.

Autonomous experimentation holds the potential to accelerate materials development by combining artificial intelligence (AI) with modular robotic platforms to explore extensive combinatorial chemical and processing spaces. Such self-driving laboratories can not only increase the throughput of repetitive experiments, but also incorporate human domain expertise to drive the search toward user-defined objectives, including improved materials performance metrics. We present an autonomous materials synthesis extension to SARA, the Scientific Autonomous Reasoning Agent, utilizing phase information provided by an automated probabilistic phase labeling algorithm to expedite the search for targeted phase regions. By incorporating human input into an expanded SARA-H (SARA with human-in-the-loop) framework, we enhance the efficiency of the underlying reasoning process. Using synthetic benchmarks, we demonstrate the efficiency of our AI implementation and show that the human input can contribute to significant improvement in sampling efficiency. We conduct experimental active learning campaigns using robotic processing of thin-film samples of several oxide material systems, including ${\text{Bi}}_2{\text{O}}_3, {\mathrm{SnO}}_x$, and $\mathrm{Bi}\text{−}\mathrm{Ti}\text{−}\text{O}$, using lateral-gradient laser spike annealing to synthesize and kinetically trap metastable phases. We showcase the utility of human-in-the-loop autonomous experimentation for the $\mathrm{Bi}\text{−}\mathrm{Ti}\text{−}\mathrm{O}$ system, where we identify extensive processing domains that stabilize $\delta \text{−}{\mathrm{Bi}}_2{\mathrm{O}}_3$ and ${\text{Bi}}_2{\text{Ti}}_2{\text{O}}_7$, explore dwell-dependent ternary oxide phase behavior, and provide evidence confirming predictions that cationic substitutional doping of ${\mathrm{TiO}}_2$ with Bi inhibits the unfavorable transformation of the metastable anatase to the ground-state rutile phase. The autonomous methods we have developed enable the discovery of new materials and new understanding of materials synthesis and properties.

Fractional quantum Hall states host emergent anyons with exotic exchange statistics, but obtaining direct access to their topological properties in real systems remains a challenge. Neural network wave functions provide a flexible computational approach, as they can represent highly correlated states without requiring a tailored basis. Here, we use the neural network variational Monte Carlo method to study the fractional quantum Hall effect on the torus and find the three degenerate ground states at filling factor $\nu =1/3$. From these, we extract the modular $S$-matrix via entanglement interferometry, a technique previously only applied to lattice models. The resulting $S$-matrix encodes the quantum dimensions, fusion rules, and exchange statistics of the emergent anyons, providing a direct numerical demonstration of the topological order. The calculated anyon properties match the well-known theoretical and experimental results. Our work establishes neural network wave functions as a powerful tool for investigating anyonic properties.

Accurate modeling of heat flux in inertial confinement fusion plasmas requires closures that remain predictive far from local equilibrium and across disparate spatial and temporal resolutions. We develop a resolution-robust machine learning heat flux closure trained on particle-in-cell simulations using a Fourier neural operator. Two nonlocal electron thermal conduction models are trained and tested. When embedded self-consistently into the electron energy equation, the learned closure faithfully reproduces the temperature evolution and shows good temporal extrapolation and generalization capability. Remarkably, models trained on coarse-resolution data accurately predict heat flux when deployed in substantially finer-resolution implicit, iterative solvers of the energy equation, significantly enhancing the practicality of embedding data-driven closures into partial differential equation solvers. These results establish a data-driven closure that bridges kinetic and fluid descriptions and provides a viable pathway for treating machine learning as an iterative solver within the radiation-hydrodynamic simulations of inertial confinement fusion plasma.

Electrides are exotic compounds in which excess electrons occupy interstitial regions of the crystal lattice and serve as anions, exhibiting exceptional properties such as low work function, high electron mobility, and strong catalytic activity. Although they show promise for diverse applications, identifying new electrides remains challenging due to the difficulty of achieving energetically favorable electron localization in crystal cavities. Here, we present an accelerated materials discovery framework that combines physical principles, diffusion-based materials generation with hierarchical thermodynamic and electronic structure screening. Using this workflow, we systematically explored 1510 binary and 6654 ternary chemical compositions containing excess valence electrons from electropositive alkaline, alkaline-earth, and early transition metals, and then filtered them with a high-throughput validation on both thermodynamical stability and electronic structure analysis. As a result, we have identified 264 new electron-rich compounds within 0.05 eV/atom above the convex hull at the density functional theory level, including 13 thermodynamically stable electrides. Our approach demonstrates a generalizable strategy for targeted materials discovery in a vast chemical space.

Moiré superlattices in two-dimensional materials exhibit rich quantum phenomena, but ab initio modeling of these systems remains computationally prohibitive. Existing machine learning methods for accelerating density-functional theory can target the prediction of different quantities and often rely on the locality assumption. Here, we train a Gaussian process regression model for symmetry-adapted learning of three-dimensional electron densities exclusively on the electron densities of small displaced bilayer structures and then extrapolate electron density prediction to the large supercells required to describe small twist angles between these bilayers. We show the necessity of long-range descriptors to yield reliable band structures and electrostatic properties of large twisted bilayer structures when these are derived from predicted densities. We demonstrate that the choice of descriptor determines the distribution of residual density errors, which in turn affects the downstream electronic properties. We apply our models to twisted bilayer graphene, hexagonal boron nitride, and transition metal dichalcogenides, focusing on the model’s capacity to predict complex phenomena, including flat-band formation, bandwidth narrowing, domain wall electric fields, and spin-orbit coupling effects. Beyond moiré materials, this approach provides a general methodology for electronic structure prediction in large-scale systems with substantial long-range phenomena related to nonlocal geometric information.

Identifying materials with strong performance in a specific application, particularly when the origin of that performance is unclear or difficult to compute, remains a central challenge in materials science. Trial-and-error exploration is prohibitively expensive due to the vastness of the materials space. A more practical strategy is to search for new materials within the proximity of known compounds exhibiting the desired property. This requires defining a meaningful representation to assess materials similarity. Structural fingerprints are commonly used, yet structural similarity often fails to translate into similarity in properties. Electronic fingerprints, such as density of states or band structure, were proposed as a better alternative, but computing them for >100 000 materials is still too costly for rapid screening. Here, we present ProDosNet, a graph convolutional network trained on atom- and orbital-resolved projected density of states (PDOS) data, capable of predicting electronic structure at extremely low computational cost. Using this model, we generated PDOS fingerprints for all compounds in the Materials Project database and clustered them by orbital-resolved PDOS similarity. We demonstrate that these electronic fingerprints allow finding materials with similar electronic properties but drastically different structures for applications in photovoltaics, catalysis, and batteries.

The requirement of generating predictions that exactly fulfill the fundamental symmetry of the corresponding physical quantities has profoundly shaped the development of machine-learning (ML) models for physical simulations. In many cases, models are built using constrained mathematical forms that ensure that symmetries are enforced exactly. However, unconstrained models that do not obey rotational symmetries are often found to have competitive performance, and to be able to learn to a high level of accuracy an approximate equivariant behavior with a simple data augmentation strategy. In this paper, we introduce rigorous metrics to measure the symmetry content of the learned representations in such models, and assess the accuracy with which the outputs fulfill the equivariant condition. We apply these metrics to two unconstrained, transformer-based models operating on decorated point clouds (a graph neural network for atomistic simulations and a PointNet-style architecture for particle physics) to investigate how symmetry information is processed across architectural layers and is learned during training. Based on these insights, we establish a rigorous framework for diagnosing spectral failure modes in ML models. Enabled by this analysis, we demonstrate that one can achieve superior stability and accuracy by strategically injecting the minimum required inductive biases, preserving the high expressivity and scalability of unconstrained architectures while guaranteeing physical fidelity.

A combination of physics-based simulation and experiments has been critical to achieving ignition in inertial confinement fusion (ICF). Simulation and experiment both produce a mixture of scalar and image outputs; however, only a subset of simulated data are available experimentally. We introduce a generative framework, called JointDiff, which enables predictions of conditional simulation input and output distributions from partial, multimodal observations. The model leverages joint diffusion to unify forward surrogate modeling, inverse inference, and output imputation into one architecture. We train our model on a large ensemble of three-dimensional multirocket piston simulations and demonstrate high accuracy, statistical robustness, and promising transfer to experiments performed at the National Ignition Facility, with further improvements achieved through experimental fine-tuning. This work establishes JointDiff as a flexible generative surrogate for multimodal scientific tasks, with implications for understanding diagnostic constraints, aligning simulation to experiment, and accelerating ICF design.

In materials science, data are scarce and expensive to generate, whether computationally or experimentally. Therefore, it is crucial to identify how model performance scales with dataset size and model capacity to distinguish between data- and model-limited regimes. Neural scaling laws provide a framework for quantifying this behavior and guide the design of materials datasets and machine learning architectures. Here, we investigate neural scaling laws for predicting the optical properties of solids, using over 200 000 dielectric functions and Drude frequencies of metals from high-throughput ab initio calculations. We study the scaling of three multiobjective graph neural network architectures trained to simultaneously predict the frequency-dependent complex interband dielectric function as a continuous spectral response and the Drude frequency as a scalar quantity. Across two rotationally invariant graph neural networks that differ in their effective body order and an equivariant graph neural network evaluated at different maximum angular degrees, we consistently observe broken neural scaling laws with respect to dataset size. In contrast, scaling with respect to the number of model parameters is well described, in all cases, by saturating power laws.

When does a fractional quantum Hall (FQH) liquid crystallize? Addressing this question requires a framework that treats fractionalization and crystallization on equal footing, especially in strong Landau-level mixing regime. Here, we introduce MagNet, a self-attention neural-network variational wavefunction designed for quantum systems in magnetic fields on the torus geometry. We show that MagNet provides a unifying and expressive ansatz capable of describing both FQH states and electron crystals within the same architecture. Trained solely by energy minimization of the microscopic Hamiltonian, MagNet discovers topological liquid and electron crystal ground states across a broad range of Landau-level mixing. Our results highlight the power of first-principles artificial intelligence (AI) for solving strongly interacting many-body problems and finding competing phases without external training data or physics preknowledge.

The flow matching has rapidly become a dominant paradigm in classical generative modeling, offering an efficient way to interpolate between two complex distributions. We extend this idea to the quantum realm and introduce the quantum flow matching (QFM), a quantum-circuit realization that offers efficient interpolation between two density matrices. QFM offers systematic preparation of density matrices and generation of samples for accurately estimating observables, and can be realized on quantum computers without the need for costly circuit redesigns. We validate its versatility on a set of applications: (1) generating target states with prescribed magnetization and entanglement entropy, (2) estimating nonequilibrium free-energy differences to test the quantum Jarzynski equality, and (3) expediting the study on superdiffusion. These results position QFM as a unifying and promising framework for generative modeling across quantum systems.

Fault-tolerant quantum computing demands decoders that are fast, accurate, and adaptable to circuit structure and realistic noise. While machine learning decoders have demonstrated impressive performance for quantum memory, their use in algorithmic decoding—where logical gates create complex error correlations—remains limited. We introduce a modular attention-based neural decoder that learns gate-induced correlations and generalizes from training on random circuits to unseen multiqubit algorithmic workloads. Our decoders achieve fast inference and logical error rates comparable to most-likely-error decoders across varied circuit depths and qubit counts. Addressing realistic noise, we incorporate loss-resolving readout, yielding substantial gains when qubit loss is present. We further show that by tailoring the decoder to the structure of the algorithm and decoding only the relevant observables, we can simplify the decoder design without sacrificing accuracy. We validate our framework on multiple error correction codes—including surface codes and two-dimensional color codes—and demonstrate state-of-the-art performance under circuit-level noise. Finally, we show that the attention mechanism learns to track physically meaningful error correlations, consistent with the expected propagation pathways through entangling gates. Enabling experimental validation of deep-circuit fault-tolerant algorithms and architectures [Bluvstein et al., Nature (London) 649, 39 (2026)], these results establish neural decoders as practical, versatile, and high-performance tools for quantum computing.

A critical contribution of artificial intelligence to materials physics is accurate and efficient predictions of crystal properties. Real-space graph neural networks are currently a mainstream choice for crystal property prediction, as reciprocal-space approaches have been commonly considered incapable of achieving comparable accuracy. Here, we develop an Angle-resolved-photoemission-spectroscopy-Inspired Reciprocal-space Crystal Property Predictor (AIRCPP), which combines spherical harmonics and Legendre polynomials as an orthogonal basis, sampled by a Lebedev grid for the reciprocal space. Using a large dataset of 95 700 materials, we demonstrate that AIRCPP achieves comparable or higher accuracy in predicting various crystal properties compared to the widely used crystal graph convolutional neural networks (CGCNN), but with much lower computational costs. Combining AIRCPP and CGCNN further enables a more powerful model termed AIRCPP-MIX that achieves comparable accuracy to the state-of-the-art advanced models. Our study demonstrates the giant potential of reciprocal-space approaches in highly accurate crystal property predictions, laying the foundation for computational materials design and discovery.

Dielectric response governs how materials interact with electric fields and light. Still, first-principles prediction of polarization $\mathbf{P}$, Born effective charges $Z^{*}$, and polarizability $\mathit{\alpha }$ remains too costly for large-scale screening and long-time dynamics. We introduce MACE-Field, a field-aware, $O\left(3\right)$-equivariant interatomic potential that learns a single electric-enthalpy functional $\mathcal{F}\left(\right\{\mathbf{R}\},\mathbf{E})$ and obtains $\mathbf{P}, Z^{*}$, and $\mathit{\alpha }$ by exact differentiation. A uniform field couples to latent equivariant features inside the MACE backbone, while the scalar energy readout preserves Maxwell reciprocity, the acoustic sum rule, and crystal tensor symmetries by construction. Because this coupling is a plug-in on top of standard MACE, existing energy/force foundation models can be upgraded to become field aware. Benchmarked against semilocal density-functional theory (DFT)/density-functional perturbation theory (DFPT) reference data, a directly trained cross-chemistry ferroelectric model reproduces the same-branch Berry phase and spontaneous polarizations across diverse inorganic crystals. Starting from the multihead foundation model mace-mp-mh-0 and its Open Materials 2024 (OMAT)-Perdew-Burke-Ernzerhof (PBE) head, joint fine-tuning on dielectric, ferroelectric, and replay data yields MACE-Field-MH-0 foundation models, which predict $Z^{*}, \mathit{\alpha }$, derived dielectric constants, and cross-chemistry polarization trends with fidelity that captures branch-resolved polarization and spontaneous polarization, while retaining strong force-field accuracy. Further, single-material MACE-Field models and MACE-Field-MH-0 reproduce ${\mathrm{BaTiO}}_3$ hysteresis loops and $\alpha$-quartz infrared, Raman, and dielectric spectra from finite-field molecular dynamics, comparable to DFPT. These results show that a simple, physics-informed field coupling can endow atomistic foundation models with transferable dielectric and ferroelectric response, while targeted single-material training remains advantageous for the most quantitative spectroscopic predictions.

Contemporary quantum devices are reaching new limits in size and complexity, allowing for the experimental exploration of emergent quantum modes. However, this increased complexity introduces significant challenges in device tuning and control. Here, we demonstrate autonomous tuning of emergent Poor Man’s Majorana zero modes in a minimal realization of a Kitaev chain. We achieve this task using cross-platform transfer learning. First, we train a tuning model on a theory model. Next, we retrain it using a Kitaev chain realization in a two-dimensional electron gas. Finally, we apply this model to tune a Kitaev chain realized in quantum dots coupled through a semiconductor-superconductor section in a one-dimensional nanowire. Utilizing a convolutional neural network, we predict the tunneling and Cooper pair splitting rates from differential conductance measurements, employing these predictions to adjust the electrochemical potential to a Poor Man’s Majorana sweet spot. The algorithm successfully converges to an immediate vicinity of a sweet spot (within $\pm 1.5\mathrm{m}\mathrm{V}$ in 67.6% of attempts and within $\pm 4.5\mathrm{m}\mathrm{V}$ in 80.9% of cases), typically finding a sweet spot in 45 min or less. This advancement is a stepping stone toward autonomous tuning of emergent modes in interacting systems, and toward foundational tuning machine learning models that can be deployed across a range of experimental platforms.

We propose a clustering approach for point cloud segmentation based on supervised contrastive metric learning (CML). Rather than predicting cluster assignments or object-centric variables, the method learns a latent representation in which points belonging to the same object are embedded nearby, while unrelated points are separated. Clusters are then reconstructed using a density-based readout in the learned metric space, decoupling representation learning from cluster formation and enabling flexible inference. The approach is evaluated on simulated data from a highly granular calorimeter, where the task is to separate highly overlapping particle showers represented as sets of calorimeter hits. A direct comparison with object condensation (OC) is performed using identical graph neural network backbones and equal latent dimensionality, isolating the effect of the learning objective. The CML method produces a more stable and separable embedding geometry for both electromagnetic and hadronic particle showers, leading to improved local neighborhood consistency, a more reliable separation of overlapping showers, and better generalization when extrapolating to unseen multiplicities and energies. This translates directly into higher reconstruction efficiency and purity, particularly in high-multiplicity regimes, as well as improved energy resolution. In mixed-particle environments, CML maintains strong performance, suggesting stable learning of the shower topology across particle types, while OC exhibits significant degradation. These results demonstrate that similarity-based representation learning combined with density-based aggregation is a promising alternative to object-centric approaches for point cloud segmentation in highly granular detectors.

van der Waals (vdW) interactions are essential for describing molecules and materials, from drug design and catalysis to battery applications. These omnipresent interactions must also be accurately included in machine-learned (ML) force fields. The many-body dispersion (MBD) method stands out as one of the most accurate and transferable approaches to capture vdW interactions, requiring only atomic $C_6$ coefficients and polarizabilities as input. We present MBD-ML, a pretrained message-passing neural network that predicts these atomic properties directly from structures with demonstrated transferability across molecular systems and organic condensed phases. Through seamless integration with libMBD, our method enables the immediate calculation of MBD-inclusive total energies, forces, and stress tensors. By eliminating the need for intermediate electronic-structure calculations, MBD-ML offers a practical and streamlined tool that simplifies the incorporation of state-of-the-art vdW interactions into any electronic-structure code, as well as empirical and machine-learned force fields.

Neural quantum states (NQS) have gained prominence in variational quantum Monte Carlo methods in approximating ground-state wavefunctions. Despite their success, they face limitations in optimization, scalability, and expressivity in addressing certain problems. In this work, we propose a quantum-neural hybrid framework that combines parametrized quantum circuits with neural networks to model quantum many-body wavefunctions. This approach combines the efficient sampling and optimization capabilities of autoregressive neural networks with the enhanced expressivity provided by quantum circuits. Numerical simulations demonstrate the scalability and accuracy of the hybrid ansatz in spin systems and quantum chemistry problems. Our results reveal that the hybrid method achieves notably lower relative energy compared to stand-alone NQS. These findings underscore the potential of quantum-neural hybrid methods for tackling challenging problems in quantum many-body simulations.

Simulations of quantum matter rely mainly on Kohn-Sham density functional theory (DFT), which often fails for strongly correlated systems. Quantum embedding (QE) theories address this limitation by mapping the system onto an auxiliary embedding Hamiltonian (EH) describing fragment-environment interactions, but the EH is typically large and its iterative solution is the primary computational bottleneck. We introduce a linear foundation model for QE that utilizes principal component analysis to compress the space of quantum states needed to solve the EH within a small variational subspace. Using a data-driven active-learning scheme, we learn this subspace from EH ground states and reduce each embedding solution to a deterministic ground-state eigenvalue problem in the reduced space. Within the ghost-Gutzwiller approximation, we show for a three-orbital Hubbard model that a variational space learned on a Bethe lattice is transferable to square and cubic lattices without additional training, while substantially reducing the cost of the EH step. We further validate the approach on plutonium, where a single variational space reproduces the energetics of all six crystalline phases while reducing the cost of the EH solution by orders of magnitude. This provides a practical route to overcome the main computational bottleneck of QE frameworks, paving the way for high-throughput ab initio simulations of strongly correlated materials at a near-DFT cost.