Machine learning force fields (MLFFs) have instigated a groundbreaking shift in molecular dynamics (MD) simulations across a wide range of fields, such as physics, chemistry, biology, and materials science. Incorporating higher order many-body interactions can enhance the expressiveness and accuracy of models. Recent models have achieved this by explicitly including up to four-body interactions. However, five-body interactions, which have relevance in various fields, are still challenging to incorporate efficiently into MLFFs. In this work, we propose the quintuple network (QuinNet), an end-to-end graph neural network that efficiently expresses many-body interactions up to five-body interactions with \emph{ab initio} accuracy. By analyzing the topology of diverse many-body interactions, we design the model architecture to efficiently and explicitly represent these interactions. We evaluate QuinNet on public datasets of small molecules, such as MD17 and its revised version, and show that it is compatible with other state-of-the-art models on these benchmarks.

Noncovalent interactions--vdW dispersion, hydrogen/halogen bonding, ion-$π$, and $π$-stacking--govern structure, dynamics, and emergent phenomena in materials and molecular systems, yet accurately learning them alongside covalent forces remains a core challenge for machine-learned force fields (MLFFs). This challenge is acute for global models that use Coulomb-matrix (CM) descriptors compared under Euclidean/Frobenius metrics in multifragment settings. We show that the mismatch between predominantly covalent force labels and the CM's overrepresentation of intermolecular features biases single-model training and degrades force-field fidelity. To address this, we introduce \textit{$Δ$-sGDML}, a scale-aware formulation within the sGDML framework that explicitly decouples intra- and intermolecular physics by training fragment-specific models alongside a dedicated binding model, then composing them at inference. Across benzene dimers, host-guest complexes (C$_{60}$@buckycatcher, NO$_3^-$@i-corona[6]arene), benzene-water, and benzene-Na$^+$, \mbox{$Δ$-sGDML} delivers consistent gains over a single global model, with fragment-resolved force-error reductions up to \textbf{75\%}, without loss of energy accuracy. Furthermore, molecular-dynamics simulations further confirm that the $Δ$-model yields a reliable force field for C$_{60}$@buckycatcher, producing stable trajectories across a wide range of temperatures (10-400~K), unlike the single global model, which loses stability above $\sim$200~K. The method offers a practical route to homogenize per-fragment errors and recover reliable noncovalent physics in global MLFFs.

Point defects play a central role in driving the properties of materials. First-principles methods are widely used to compute defect energetics and structures, including at scale for high-throughput defect databases. However, these methods are computationally expensive, making machine-learning force fields (MLFFs) an attractive alternative for accelerating structural relaxations. Most existing MLFFs are based on graph neural networks (GNNs), which can suffer from oversmoothing and poor representation of long-range interactions. Both of these issues are especially of concern when modeling point defects. To address these challenges, we introduce the Accelerated Deep Atomic Potential Transformer (ADAPT), an MLFF that replaces graph representations with a direct coordinates-in-space formulation and explicitly considers all pairwise atomic interactions. Atoms are treated as tokens, with a Transformer encoder modeling their interactions. Applied to a dataset of silicon point defects, ADAPT achieves a roughly 33 percent reduction in both force and energy prediction errors relative to a state-of-the-art GNN-based model, while requiring only a fraction of the computational cost.

Artificial intelligence (AI) is revolutionizing scientific research, particularly in computational materials science, by enabling more accurate and efficient simulations. Machine learning force fields (MLFFs) have emerged as powerful tools for molecular dynamics (MD) simulations, potentially offering quantum-mechanical accuracy with the efficiency of classical MD. This Perspective evaluates the viability of universal MLFFs for simulating complex materials systems from the standpoint of a potential practitioner. Using the temperature-driven ferroelectric-paraelectric phase transition of PbTiO$_3$ as a benchmark, we assess leading universal force fields, including CHGNet, MACE, M3GNet, and GPTFF, alongside specialized models like UniPero. While universal MLFFs trained on PBE-derived datasets perform well in predicting equilibrium properties, they largely fail to capture realistic finite-temperature phase transitions under constant-pressure MD, often exhibiting unphysical instabilities. These shortcomings stem from inherited biases in exchange-correlation functionals and limited generalization to anharmonic interactions governing dynamic behavior. However, fine-tuning universal models or employing system-specific MLFFs like UniPero successfully restores predictive accuracy. We advocates for hybrid approaches combining universal pretraining with targeted optimization, improved error quantification frameworks, and community-driven benchmarks to advance MLFFs as robust tools for computational materials discovery.

Machine Learning Force Fields (MLFFs) are a promising alternative to expensive ab initio quantum mechanical molecular simulations. Given the diversity of chemical spaces that are of interest and the cost of generating new data, it is important to understand how MLFFs generalize beyond their training distributions. In order to characterize and better understand distribution shifts in MLFFs, we conduct diagnostic experiments on chemical datasets, revealing common shifts that pose significant challenges, even for large foundation models trained on extensive data. Based on these observations, we hypothesize that current supervised training methods inadequately regularize MLFFs, resulting in overfitting and learning poor representations of out-of-distribution systems. We then propose two new methods as initial steps for mitigating distribution shifts for MLFFs. Our methods focus on test-time refinement strategies that incur minimal computational cost and do not use expensive ab initio reference labels. The first strategy, based on spectral graph theory, modifies the edges of test graphs to align with graph structures seen during training. Our second strategy improves representations for out-of-distribution systems at test-time by taking gradient steps using an auxiliary objective, such as a cheap physical prior. Our test-time refinement strategies significantly reduce errors on out-of-distribution systems, suggesting that MLFFs are capable of and can move towards modeling diverse chemical spaces, but are not being effectively trained to do so. Our experiments establish clear benchmarks for evaluating the generalization capabilities of the next generation of MLFFs. Our code is available at https://tkreiman.github.io/projects/mlff_distribution_shifts/.

Highly accurate force fields are a mandatory requirement to generate predictive simulations. In this regard, Machine Learning Force Fields (MLFFs) have emerged as a revolutionary approach in computational chemistry and materials science, combining the accuracy of quantum mechanical methods with computational efficiency orders of magnitude superior to ab-initio methods. This chapter provides an introduction of the fundamentals of learning and how it is applied to construct MLFFs, detailing key methodologies such as neural network potentials and kernel-based models. Emphasis is placed on the construction of SchNet model, as one of the most elemental neural network-based force fields that are nowadays the basis of modern architectures. Additionally, the GDML framework is described in detail as an example of how the elegant formulation of kernel methods can be used to construct mathematically robust and physics-inspired MLFFs. The ongoing advancements in MLFF development continue to expand their applicability, enabling precise simulations of large and complex systems that were previously beyond reach. This chapter concludes by highlighting the transformative impact of MLFFs on scientific research, underscoring their role in driving future discoveries in the fields of chemistry, physics, and materials science.

Machine learning force fields (MLFFs) have instigated a groundbreaking shift in molecular dynamics (MD) simulations across a wide range of fields, such as physics, chemistry, biology, and materials science. Incorporating higher order many-body interactions can enhance the expressiveness and accuracy of models. Recent models have achieved this by explicitly including up to four-body interactions. However, five-body interactions, which have relevance in various fields, are still challenging to incorporate efficiently into MLFFs. In this work, we propose the quintuple network (QuinNet), an end-to-end graph neural network that efficiently expresses many-body interactions up to five-body interactions with \emph{ab initio} accuracy. By analyzing the topology of diverse many-body interactions, we design the model architecture to efficiently and explicitly represent these interactions.

The foundation model (FM) paradigm is transforming Machine Learning Force Fields (MLFFs), leveraging general-purpose representations and scalable training to perform a variety of computational chemistry tasks. Although MLFF FMs have begun to close the accuracy gap relative to first-principles methods, there is still a strong need for faster inference speed. Additionally, while research is increasingly focused on general-purpose models which transfer across chemical space, practitioners typically only study a small subset of systems at a given time. This underscores the need for fast, specialized MLFFs relevant to specific downstream applications, which preserve test-time physical soundness while maintaining train-time scalability. In this work, we introduce a method for transferring general-purpose representations from MLFF foundation models to smaller, faster MLFFs specialized to specific regions of chemical space. We formulate our approach as a knowledge distillation procedure, where the smaller "student" MLFF is trained to match the Hessians of the energy predictions of the "teacher" foundation model. Our specialized MLFFs can be up to 20 $\times$ faster than the original foundation model, while retaining, and in some cases exceeding, its performance and that of undistilled models. We also show that distilling from a teacher model with a direct force parameterization into a student model trained with conservative forces (i.e., computed as derivatives of the potential energy) successfully leverages the representations from the large-scale teacher for improved accuracy, while maintaining energy conservation during test-time molecular dynamics simulations. More broadly, our work suggests a new paradigm for MLFF development, in which foundation models are released along with smaller, specialized simulation "engines" for common chemical subsets.

Machine-learned force fields (MLFFs) promise to offer a computationally efficient alternative to ab initio simulations for complex molecular systems. However, ensuring their generalizability beyond training data is crucial for their wide application in studying solid materials. This work investigates the ability of a graph neural network (GNN)-based MLFF, trained on Lennard-Jones Argon, to describe solid-state phenomena not explicitly included during training. We assess the MLFF's performance in predicting phonon density of states (PDOS) for a perfect face-centered cubic (FCC) crystal structure at both zero and finite temperatures. Additionally, we evaluate vacancy migration rates and energy barriers in an imperfect crystal using direct molecular dynamics (MD) simulations and the string method. Notably, vacancy configurations were absent from the training data. Our results demonstrate the MLFF's capability to capture essential solid-state properties with good agreement to reference data, even for unseen configurations. We further discuss data engineering strategies to enhance the generalizability of MLFFs. The proposed set of benchmark tests and workflow for evaluating MLFF performance in describing perfect and imperfect crystals pave the way for reliable application of MLFFs in studying complex solid-state materials.

A force field as accurate as quantum mechanics (QM) and as fast as molecular mechanics (MM), with which one can simulate a biomolecular system efficiently enough and meaningfully enough to get quantitative insights, is among the most ardent dreams of biophysicists -- a dream, nevertheless, not to be fulfilled any time soon. Machine learning force fields (MLFFs) represent a meaningful endeavor towards this direction, where differentiable neural functions are parametrized to fit ab initio energies, and furthermore forces through automatic differentiation. We argue that, as of now, the utility of the MLFF models is no longer bottlenecked by accuracy but primarily by their speed (as well as stability and generalizability), as many recent variants, on limited chemical spaces, have long surpassed the chemical accuracy of $1$ kcal/mol -- the empirical threshold beyond which realistic chemical predictions are possible -- though still magnitudes slower than MM. Hoping to kindle explorations and designs of faster, albeit perhaps slightly less accurate MLFFs, in this review, we focus our attention on the design space (the speed-accuracy tradeoff) between MM and ML force fields. After a brief review of the building blocks of force fields of either kind, we discuss the desired properties and challenges now faced by the force field development community, survey the efforts to make MM force fields more accurate and ML force fields faster, envision what the next generation of MLFF might look like.