Machine learning interatomic potentials, particularly those based on deep equivariant neural networks, have demonstrated state-of-the-art accuracy and computational efficiency in atomistic modeling tasks like molecular dynamics and high-throughput screening. The size of datasets and demands of downstream workflows are growing rapidly, making robust and scalable software essential. This work presents a major overhaul of the NequIP framework focusing on multi-node parallelism, computational performance, and extensibility. The redesigned framework supports distributed training on large datasets and removes barriers preventing full utilization of the PyTorch 2.0 compiler at train time. We demonstrate this acceleration in a case study by training Allegro models on the SPICE 2 dataset of organic molecular systems. For inference, we introduce the first end-to-end infrastructure that uses the PyTorch Ahead-of-Time Inductor compiler for machine learning interatomic potentials. Additionally, we implement a custom kernel for the Allegro model's most expensive operation, the tensor product. Together, these advancements speed up molecular dynamics calculations on system sizes of practical relevance by up to a factor of 18.

Similar to other perovskites in its family, SrTiO$_3$ exhibits a significant softening of the ferroelectric mode with decreasing temperature, a behavior that typically heralds the onset of a ferroelectric transition. However, this material remains paraelectric down to 0K due to the Heisenberg quantum uncertainty principle that prevents atoms from localizing in the ferroelectric minima, a fundamental limit that appears impossible to overcome. This work shows that in the strong out-of-equilibrium regime induced by resonant mid-IR pulses, quantum fluctuations can be suppressed, effectively cooling the material below the 0K ground state and inducing a ferroelectric transition in SrTiO$_3$ that is otherwise impossible. The appearance of a metastable state, that is distinct from the conventional ground state, is the first demonstration of how it is possible to leverage and control quantum fluctuations with pulsed light to qualitatively alter the free energy landscape of a quantum system. We predict the conditions and system parameter under which induced non-equilibrium state can be long-lived and even permanent. In providing a quantitative description, based on first principles machine learned potential energy surface, we explain recent experimental observations of light-induced ferroelectric transition in this material.

We present a differentiable formalism for learning free energies that is capable of capturing arbitrarily complex model dependencies on coarse-grained coordinates and finite-temperature response to variation of general system parameters. This is done by endowing models with explicit dependence on temperature and parameters and by exploiting exact differential thermodynamic relationships between the free energy, ensemble averages, and response properties. Formally, we derive an approach for learning high-dimensional cumulant generating functions using statistical estimates of their derivatives, which are observable cumulants of the underlying random variable. The proposed formalism opens ways to resolve several outstanding challenges in bottom-up molecular coarse graining dealing with multiple minima and state dependence. This is realized by using additional differential relationships in the loss function to significantly improve the learning of free energies, while exactly preserving the Boltzmann distribution governing the corresponding fine-grain all-atom system. As an example, we go beyond the standard force-matching procedure to demonstrate how leveraging the thermodynamic relationship between free energy and values of ensemble averaged all-atom potential energy improves the learning efficiency and accuracy of the free energy model. The result is significantly better sampling statistics of structural distribution functions. The theoretical framework presented here is demonstrated via implementations in both kernel-based and neural network machine learning regression methods and opens new ways to train accurate machine learning models for studying thermodynamic and response properties of complex molecular systems.

The design of better exchange-correlation functionals for Density Functional Theory (DFT) is a central challenge of modern electronic structure theory. However, current developments are limited by the mathematical form of the functional, with efficient semilocal functionals being inaccurate for many technologically important systems and the more accurate hybrid functionals being too expensive for large solid-state systems due to the use of the exact exchange operator. In this work, we use machine learning combined with exact physical constraints to design an exchange functional that is both orbital-dependent and nonlocal, but which can be evaluated at roughly the cost of semilocal functionals and is significantly faster than hybrid DFT in plane-wave codes. By training functionals with several different feature sets, we elucidate the roles of orbital-dependent and nonlocal features in learning the exchange energy and determine that both types of features provide vital and independently important information to the model. Having trained our new exchange functional with an expressive, nonlocal feature set, we substitute it into existing hybrid functionals to achieve hybrid-DFT accuracy on thermochemical benchmark sets and improve the accuracy of band gap predictions over semilocal DFT. To demonstrate the scalability of our approach as well as the practical benefits of improved band gap prediction, we compute charged defect transition levels in silicon using large supercells. Due to its transferability and computational efficiency for both molecular and extended systems, our model overcomes the cost-accuracy trade-off between semilocal and hybrid DFT, and our general approach provides a feasible path toward a universal exchange-correlation functional with post-hybrid DFT accuracy and semilocal DFT cost.

The systematic underestimation of band gaps is one of the most fundamental challenges in semilocal density functional theory (DFT). In addition to hindering the application of DFT to predicting electronic properties, the band gap problem is intimately related to self-interaction and delocalization errors, which make the study of charge transfer mechanisms with DFT difficult. In this work, we present two key innovations to address the band gap problem. First, we design an approach for machine learning density functionals based on Gaussian processes to explicitly fit single-particle energy levels. Second, we introduce novel nonlocal features of the density matrix that are expressive enough to fit these single-particle levels. Combining these developments, we train a machine-learned functional for the exact exchange energy that predicts molecular energy gaps and reaction energies of a wide range of molecules in excellent agreement with reference hybrid DFT calculations. In addition, while being trained solely on molecular data, our model predicts reasonable formation energies of polarons in solids, showcasing its transferability and robustness. Our approach generalizes straightforwardly to full exchange-correlation functionals, thus paving the way to the design of novel state-of-the-art functionals for the prediction of electronic properties of molecules and materials.

Metal surfaces have long been known to reconstruct, significantly influencing their structural and catalytic properties. Many key mechanistic aspects of these subtle transformations remain poorly understood due to limitations of previous simulation approaches. Using active learning of Bayesian machine-learned force fields trained from ab initio calculations, we enable large-scale molecular dynamics simulations to describe the thermodynamics and time evolution of the low-index mesoscopic surface reconstructions of Au (e.g., the Au(111)-`Herringbone,' Au(110)-(1$\times$2)-`Missing-Row,' and Au(100)-`Quasi-Hexagonal' reconstructions). This capability yields direct atomistic understanding of the dynamic emergence of these surface states from their initial facets, providing previously inaccessible information such as nucleation kinetics and a complete mechanistic interpretation of reconstruction under the effects of strain and local deviations from the original stoichiometry. We successfully reproduce previous experimental observations of reconstructions on pristine surfaces and provide quantitative predictions of the emergence of spinodal decomposition and localized reconstruction in response to strain at non-ideal stoichiometries. A unified mechanistic explanation is presented of the kinetic and thermodynamic factors driving surface reconstruction. Furthermore, we study surface reconstructions on Au nanoparticles, where characteristic (111) and (100) reconstructions spontaneously appear on a variety of high-symmetry particle morphologies.

The electron self-interaction problem in density functional theory affects the accurate modeling of polarons, particularly their localization and formation energy. Charged and neutral density functional formulations have been developed to address this issue, yet their relationship remains unclear. Here, we demonstrate their equivalence in treating the many-body self-interaction of the polaron state. In particular, we connect with each other piecewise-linear functionals based on adding an extra charge to the supercell, the pSIC approach derived from the energetics of the neutral defect with polaronic distortions in a supercell, and the unit-cell method for polarons based on electron-phonon couplings. We show that these approaches lead to the same formal expression of the self-interaction corrected energy, which is fully defined by the energetics of the neutral charge state of the charged polaronic structure. Residual differences between these methods solely arise from the achieved polaronic structure, which is affected by different treatments of electron-screening and finite-size effects. We apply these methods to a set of prototypical small hole and electron polarons, including the hole polaron in MgO, the hole polaron in $\beta$-Ga$_2$O$_3$, the $V_\text{k}$ center in NaI, the electron polaron in BiVO$_4$, and the electron polaron in TiO$_2$. We show that the ground-state properties of polarons obtained using charged and neutral density functional formulations are in excellent agreement.