We introduce a variational wave function based on neural-network quantum states (NQS) to study lattice systems whose local Hilbert space contains both spin and fermionic degrees of freedom. Our approach is based on the use of the transformer architecture, which can naturally handle composite local Hilbert spaces through a tokenization procedure closely inspired by techniques from natural language processing. The key methodological innovation is that the neural network predicts a set of fermionic orbitals that depend on the spin configuration in a backflow-inspired manner. We apply the method to the one-dimensional ancilla layer model, consisting of a chain of mobile spin-$1/2$ fermions coupled to a two-leg spin-$1/2$ ladder. For open boundary conditions, we achieve excellent quantitative agreement with density matrix renormalization group results across the full range of parameters considered. We find a phase in which the chain forms an effectively decoupled Luttinger liquid (LL), and an ${\mathrm{LL}}^{*}$ phase with a distinct Fermi wave vector in which the mobile fermions are Kondo screened by one leg of the ladder, while the other leg forms the critical Bethe spin liquid. The ${\mathrm{LL}}^{*}$ is the analog of the ${\mathrm{FL}}^{*}$ phase in two dimensions proposed to describe the cuprate pseudogap. We also find a Luther-Emery phase, where the ${\mathrm{LL}}^{*}$ state becomes unstable toward the formation of a spin gap. The transformer ansatz maintains comparable accuracy for periodic boundary conditions, where tensor-network methods are computationally more demanding. Moreover, we show that the approach extends naturally to fully periodic two-dimensional clusters, a regime beyond the reach of current tensor-network methods. Together, these findings establish transformer-based NQS as an accurate and scalable variational framework for correlated lattice systems with composite local Hilbert spaces and highlight its potential for studying higher-dimensional models where boundary effects and heterogeneous local structures pose significant challenges.

There has been a veritable explosion of methods and software to perform machine-learned regression on datasets of electronic energies and forces to develop high-dimensional machine-learned potential energy surfaces (ML-PESs). A major, but not deeply studied aspect is how well different ML-PESs represent the same dataset on which they were trained, beyond the standard statistical precision measures. Here, this is examined using several “stress tests,” for two widely used machine-learned potential approaches. One is based on permutationally invariant polynomial linear least-square regression and the other is the message-passing neural network PhysNet approach. The energies from the two PESs are directly compared as are the IR spectra determined from vibrational self-consistent field/vibrational configuration interaction calculations using fitted dipole moment surfaces. In addition, tunneling splittings for the hydrogen transfer between two equivalent structures are reported using three different methods: ring polymer instanton theory, diffusion Monte Carlo simulations, and the $Q_{im}$-path method. These calculations require the evaluation of on the order of one billion energies that are widely dispersed in the 15-dimensional configurational space. The two PESs yield results for these quantities in excellent agreement with each other.

While deep learning offers powerful capabilities for scientific research, its application is often hindered by a lack of quantitative reliability. To address this, we introduce a probabilistic denoising framework that simultaneously extracts denoised signals and element-wise predictive uncertainties from noisy data. We demonstrate this approach on three-dimensional angle-resolved photoemission spectroscopy data, showing that the model reliably recovers the spectral features of a cuprate superconductor from Poisson-distributed noise with an average count of only 0.02 electrons per voxel. Crucially, we show that these predicted uncertainties can be propagated into subsequent superconducting gap analyses, enabling quantitative parameter extraction with scientifically meaningful error bars. Furthermore, we validate the broad applicability of our approach by successfully extending it to two-dimensional x-ray diffraction data. Ultimately, this approach establishes uncertainty-aware deep learning not merely as a visualization tool, but as a rigorous framework for scientific data analysis.

Foundation models build an effective representation of data that can be deployed on diverse downstream tasks. Previous research showed that the OmniLearned, a foundation model for collider physics, could significantly advance discovery potential across collider experiments. In this paper, we show that foundation models trained on collider data can transfer to cosmology. Specifically, we improve the prediction of cosmological parameters and halo and galaxy velocities in different datasets from CosmoBench. To the best of our knowledge, this is the first time a collider physics model has been shown to generalize across scientific fields.

Using a statistical mechanics framework, we investigate the parameter space of transformer models trained on protein sequence data. We sample the loss landscape at varying temperatures using Langevin dynamics to characterize the low-loss manifold and to understand the mechanisms underlying transformers’ superior performance in protein structure prediction. We find that, at variance with networks not based on the attention mechanism, the lack of a first-order-like transition in the loss of the transformer produces a range of intermediate temperatures with good learning properties; this is true for both synthetic and natural protein sequences. We also show that the parameters of most layers are highly conserved at these temperatures if the dimension of the embedding is optimal, and we provide an operative way to find this dimension. Additionally, we show that the attention matrix is more predictive of the contact maps of the protein at higher temperatures and for higher dimensions of the embedding than those optimal for learning. Finally, we showed that the models sampled at intermediate temperatures can predict the free-energy variation upon mutation, better than models obtained through standard optimization techniques.

The next generation of particle physics experiments will face an era of challenges in data acquisition, due to unprecedented data rates and volumes along with extreme environments and operational constraints. Harnessing these data for scientific discovery demands real-time inference and decision-making, intelligent data reduction, and efficient processing architectures beyond current capabilities. Crucial to the success of this experimental paradigm are several emerging technologies, such as artificial intelligence and machine learning, silicon microelectronics, and the advent of quantum algorithms and processing. Their intersection includes areas of research such as low-power and low-latency devices for edge computing, heterogeneous accelerator systems, reconfigurable hardware, codesign and synthesis strategies, readout for cryogenic or high-radiation environments, and analog computing. This white paper presents a community-driven vision to identify and prioritize research and development opportunities in hardware-based ML systems and corresponding physics applications, contributing toward a successful transition to the data frontier of fundamental science.

Extracting interpretable mathematical models from complex dynamical systems is difficult, especially for chaotic dynamics observed with noisy experimental data. We present PEM-UDE, a method that combines prediction-error methodology with universal differential equations to discover governing equations from limited, noise-corrupted observations. Prediction-error feedback smooths the chaotic optimization problem; for noise-free data generated within the model class, it preserves the data-consistent zero-loss set, whereas noise and model misspecification introduce a gain-dependent stability-bias trade-off. Preservation of the zero-loss set is not a guarantee of unique structural identifiability. We test the method on two benchmark chaotic systems—the Rössler attractor and a real electrical circuit—and recover the correct functional forms even when one observed dimension contains noise of 5 times the signal magnitude. The method also accepts prior knowledge of the system as an initial functional form, which we use to learn neural circuit equations that account for sparse connectivity, a feature missing from conventional neural mass models. Applied to a population of Izhikevich neurons, PEM-UDE yields a multiscale neural mass model that ties single-neuron parameters to macroscopic network dynamics and predicts a relationship between connection density, dominant oscillation frequency, and synchrony. We test these predictions against three intracranial recording datasets from rat and human cortices. For the neuroscience application, the learned equations are a reduced-order closure for a specified simulated Izhikevich network family; the experimental recordings provide an indirect consistency check of predicted frequency and synchrony trends, not a direct fit of the equations to recordings.

The recent development of Neural Quantum States (NQS) has established them as one of the most accurate methods for studying strongly correlated many-fermion systems, outperforming existing many-body approaches for large systems. However, NQS calculations are currently highly resource intensive. In this work, we introduce an improved Pareto frontier of efficiency and accuracy for NQS in the simulation of strongly correlated lattice fermions. This frontier is defined by two complementary backflow-related architectures: the Sparse Convolutional Ansatz for Lattice Electrons (SCALE), which achieves high computational efficiency, and the Accurate Convolutional ansatz for lattice Electrons (ACE), which delivers high variational accuracy, based on benchmark results on the Hubbard model and the $t\text{–}J$ model on large lattice sizes. SCALE utilizes a tailored convolutional design to enable an efficient local update based on the low-rank update of determinants. This structure reduces the computational scaling from $\mathcal{O}\left(N^4\right)$ to $\mathcal{O}\left(N^3\right)$ in backflow methods, resulting in a practical speedup exceeding $40\times$ in our test cases while retaining accurate variational accuracy. As an application, we study the $1/8$-doped pure Hubbard model up to size $32\times 32$ and find no significant energy difference between the horizontal and vertical unit-filled stripe states, in contrast to the half-filled stripe state when next-nearest-neighbor hoppings are included. ACE, conversely, employs a deep convolutional stack to maximize expressive power, achieving high accuracy on large systems. We perform extensive benchmark calculations on the Hubbard and $t\text{–}J$ models with the two architectures. On the challenging repulsive Hubbard model, SCALE achieves variational energies competitive with leading methods at a fraction of the computational cost. Meanwhile, ACE achieves lower variational energies than previously reported results while requiring only one-sixth of the run-time for system size $16\times 4$. These NQS approaches provide scalable, affordable, and accurate tools for exploring the rich physics of strongly correlated fermionic systems.

We present Denario, an Artificial Intelligence (AI) multiagent system designed to serve as a scientific research assistant. Denario can perform many different tasks, such as generating ideas, checking the literature, developing research plans, writing and executing code, making plots, and drafting a scientific paper. The system has a modular architecture, allowing it to handle specific tasks, such as generating an idea or carrying out near end-to-end scientific analysis using Cmbagent as a deep-research backend (end-to-end except for the novelty assessment, which is intentionally left for the user to inspect). In this work, we describe in detail Denario and its modules, and illustrate its capabilities by presenting multiple AI-generated papers generated by it in many different scientific disciplines such as astrophysics, biology, biophysics, biomedical informatics, chemistry, material science, mathematical physics, medicine, neuroscience, and planetary science. Denario can also produce work that combines ideas from different disciplines, which we illustrate with a single ($N=1$) example: a paper that applies methods from quantum physics and machine learning to astrophysical data. We report the evaluations performed on these papers by domain experts, who provided both numerical scores and reviewlike feedback. These papers were scored by domain experts on our team; we report these scores as an indicative self-assessment rather than an independent evaluation, and we flag the resulting conflict of interest explicitly. Most drafts were rated above the midpoint of a 0–10 scale, with several rated 8–9, indicating that the generated papers reach the level a good undergraduate or early graduate student could achieve after weeks or a few months of work. They should be regarded as first drafts that require expert development, not publication-ready papers. We also document an important failure mode in which, when the input data cannot be read, the system may silently generate synthetic data, which we flag explicitly as a key limitation. We then highlight the strengths, weaknesses, and limitations of the current system. Finally, we discuss the ethical implications of AI-driven research and reflect on how such technology relates to the philosophy of science. We publicly release the code at https://github.com/AstroPilot-AI/Denario. A Denario demo can also be run directly on the web at https://huggingface.co/spaces/astropilot-ai/Denario, and the full app will be deployed on the cloud.

Existing approaches to explicit data-driven discovery of nonlinear dynamical systems face a curse of dimensionality because candidate libraries grow combinatorially with system dimension. This challenge is particularly severe for high-dimensional systems arising from spatially discretized fields and large complex networks. We develop sparse regression embedded interpretable network (SREINet), a machine-learning framework that embeds sparse regression in an interpretable neural network and uses a sparsity-promoting periodic pruning scheme. Across six paradigmatic systems, SREINet accurately identifies velocity fields with more than 100 dimensions and extrapolates coherent structures from untrained data. Head-to-head benchmarks against representative equation-discovery and predictive methods on clean and noisy systems show that SREINet combines scalable computation with accurate, parsimonious equation recovery, particularly in high-dimensional settings. We further validate the framework using empirical data from a triple-pendulum experiment. These results demonstrate a practical route toward interpretable model discovery for large-scale nonlinear systems and suggest that the framework can be extended to systems with thousands of dimensions.

Tip-Enhanced Raman Spectroscopy (TERS) provides nanoscale chemical fingerprints alongside high-resolution topographic mapping of molecules, offering a powerful tool for materials discovery. However, TERS image datasets are challenging to interpret and typically demand time-consuming, computationally intensive quantum-chemistry calculations. To overcome this problem, we present an encoder-decoder model trained and evaluated on simulated TERS images of planar molecules, enabling direct prediction of molecular structures from spectral simulated data with high accuracy. Our approach demonstrates the feasibility of automating molecular structure identification from TERS images, bypassing traditional manual analysis. These findings provide a foundation for extending machine learning methods to experimental TERS datasets, potentially accelerating molecular discovery by integrating nanoscale spectroscopy with automated computational analysis.

Backpropagation learning algorithm, the workhorse of modern artificial intelligence, is notoriously difficult to implement in physical neural networks. Equilibrium propagation (EP) is an alternative with comparable efficiency and strong potential for in situ training. We extend EP learning to both discrete and continuous complex-valued wave systems. In contrast to previous EP implementations, our scheme is valid in the weakly dissipative regime and readily applicable to a wide range of physical settings, even without well-defined nodes, where trainable internode connections can be replaced by trainable local potential. We test the method in driven-dissipative exciton-polariton condensates governed by generalized Gross-Pitaevskii dynamics. Numerical studies on standard benchmarks, including a simple logical task and handwritten-digit recognition, demonstrate stable convergence, establishing a practical route to in situ learning in physical systems in which system control is restricted to local parameters.

Efficient sampling from Boltzmann distributions over discrete variables is a fundamental operation in a wide range of applications. While fast non-Markov chain Monte Carlo (MCMC) samplers have recently emerged as promising alternatives to conventional MCMC methods, their practical use for probabilistic learning remains hindered by the difficulty of estimating the effective temperature of the generated samples. In this work, we begin by introducing Langevin simulated bifurcation (LSB), a Boltzmann sampler that enables fast and parallel sampling with accuracy comparable to sequential MCMC methods. To address the challenge of unknown effective temperature, we propose conditional expectation matching (CEM), an efficient estimation method applicable to energy-based models (EBMs) with exploitable conditional independence structures. Building on these components, we further develop a learning framework, termed sampler adaptive learning (SAL), which adaptively adjusts the model temperature to match that of the distribution induced by fast non-MCMC sampling. We demonstrate the effectiveness of LSB, CEM, and SAL on semirestricted Boltzmann machines (SRBMs), a class of EBMs that are difficult to train using conventional approaches. LSB achieves orders-of-magnitude acceleration over Gibbs sampling while maintaining comparable or higher accuracy, and CEM enables accurate temperature estimation of the resulting distribution with negligible computational overhead. As a consequence, SAL enables efficient training of SRBMs and outperforms conventional Boltzmann machine learning methods on synthetic spin-glass datasets. In addition, the trained models achieve strong performance across multiple tasks, including image generation, reconstruction, and classification. These results establish LSB as a fast and accurate Boltzmann sampler and provide key insights that enable practical applications of fast non-MCMC sampling methods via efficient temperature estimation with CEM.

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.