Foundational ML Potentials

• Foundational machine learning potentials are large pre-trained models that predict interatomic potential energy surfaces with DFT-level accuracy using symmetry-preserving descriptors.
• They leverage scaling paradigms from NLP and vision alongside equivariant graph neural networks and atomic cluster expansions for broad transferability across chemical and materials systems.
• These models accelerate atomistic simulations by delivering significant speedups over traditional DFT and enabling multi-fidelity integration for diverse molecular and materials applications.

Foundational machine learning potentials (MLPs)—often termed “foundational models” or “foundation models” in recent literature—are large, pre-trained machine-learned interatomic potentials designed to provide universal, high-fidelity surrogate models of potential energy surfaces (PES) across vast chemical and materials domains. Rooted in data- and model-scaling paradigms initially developed in NLP and computer vision, these models are trained on heterogeneous quantum-mechanical data, leveraging expressive and symmetry-respecting architectures such as equivariant graph neural networks (GNNs), atomic cluster expansions, and invariant message-passing frameworks. Their goal is to deliver DFT-level (or beyond) accuracy and transferability with linear scaling, enabling robust simulations, accelerated structure/property search, and multi-fidelity integration for molecules, materials, and molecular interfaces.

1. Theoretical Framework and Statistical Foundations

All modern MLPs are formulated as high-dimensional regression tasks, approximating the Born–Oppenheimer PES $E(\mathbf{R})$ and its gradient (forces) for atomic coordinates $\mathbf{R} = (\mathbf{r}_1, \ldots, \mathbf{r}_N)$ (Thiemann et al., 1 Oct 2024). The universal ansatz decomposes the total potential energy into atom-centered (or graph neighborhood-centered) local energies: $$E_{\rm tot}(\mathbf{R}) \approx \sum_i \mathcal{M}(G_i[\mathbf{R}])$$ where $G_i$ encodes the local environment of atom $i$ via symmetry-preserving descriptors. Foundational MLPs extend this decomposition with body-ordered invariants, graph-based message passing, or explicit multi-fidelity conditioning.

The statistical underpinning aligns with classical uniform convergence theory, ensuring that the empirical risk $\hat{R}_n(f)$ converges to the expected (true) risk $R(f)$ as the number of diverse training structures $n$ grows, provided the model complexity $\mathcal{C}$ is appropriately controlled (Zhang et al., 2022). Empirical scaling laws further quantify error decay as a function of both dataset size $N_\text{data}$ and parameter count $N_\text{params}$: $$\text{Error}(N_\text{data}, N_\text{params}) \propto N_\text{data}^{-\alpha} N_\text{params}^{-\beta}$$ with $\alpha \sim 0.25-0.5$, $\beta \sim 0.1-0.3$ for modern GNN-based MLPs (Yuan et al., 13 Mar 2025).

2. Principal Architectures and Model Classes

Model Family	Local Representation	Key Properties / Scaling
Behler–Parrinello HD-NNP	Atom-centered symmetry funcs.	O(N), element-specific MLP
GNN (e.g. MACE, NequIP)	Message-passing, equivariant	O(N), high body-order, E(3) symm.
Atomic Cluster Expansion	Complete local invariant basis	Systematic improvability
SOAP/GAP	Kernel-based, SOAP descriptors	Non-parametric, GPR uncertainty
DeePMD	Local frame + deep NN	Deeplearning, channelized by species
GRACE	Graph atomic cluster expansion	Complete basis, Pareto efficiency

HD-NNP-type models rely on fixed descriptors and element-wise MLPs (Thiemann et al., 1 Oct 2024), GNN approaches (MACE, NequIP, Equiformer) encode both equivariant high-body order and message-passing, while ACE and GRACE explicitly construct a mathematically complete, orthonormal invariant basis over local atomic graphs (Lysogorskiy et al., 25 Aug 2025). Multi-fidelity “all-in-one” models such as AIO-ANI integrate quantum-chemical level as an additional input modality, supporting prediction across semi-empirical, DFT, and coupled-cluster reference energies in a unified architecture (Chen et al., 18 Sep 2024). Kernel methods (e.g., GAP) provide built-in uncertainty quantification but are primarily limited by scaling in training set size.

3. Training Strategies, Data Pipelines, and Meta-Learning

Construction of foundational MLPs necessitates assembling vast, diverse datasets—on the order of $10^7$–$10^8$ distinct configurations—covering elements, chemical bonding motifs, electronic/spin states, and off-equilibrium trajectories (Yuan et al., 13 Mar 2025). Key procedural elements include:

• Supervised pre-training: Minimize joint loss in energies, forces, and optionally stress tensors over labeled quantum-chemical data (Fabritiis, 17 Aug 2024, Chen et al., 18 Sep 2024).
• Multi-level, multimodal, and meta-learning: Ingest datasets at diverse fidelity (semi-empirical, DFT, CCSD(T)), employing explicit conditioning (feature-wise linear modulation, one-hot encoding) or meta-learning protocols (Reptile, MAML) to rapidly adapt shared representations to new reference tasks while suppressing catastrophic forgetting (Allam et al., 27 Oct 2025, Allen et al., 2023, Chen et al., 18 Sep 2024).
• Active learning/data distillation: Use ensemble-based uncertainty quantification to select maximally informative configurations from extended-ensemble MD, dramatically reducing redundant labeling cost while preserving transferability (Jung et al., 2023).
• Fine-tuning and distillation: For application-specific tasks (e.g., defect energetics, migration barriers, phase transitions), foundation models can be efficiently fine-tuned on small target datasets (usually $\mathcal{O}(10^2\text{--}10^4)$), or distilled into lightweight “student” models for accelerated inference (Lysogorskiy et al., 25 Aug 2025, Fuchs et al., 3 Dec 2025).

Reference and benchmark datasets include OMat24 (110M DFT calculations), Materials Project (MPtrj), Open Catalyst 2020 (OC20), ANI-family molecules, Alexandria, and newly curated multi-task molecular mixes (100M molecules, 3,000+ tasks) (Lysogorskiy et al., 25 Aug 2025, Beaini et al., 2023).

4. Transferability, Multi-Task Robustness, and Uncertainty Quantification

Foundational MLPs are designed for broad transferability across chemical compound classes, structural motifs, and property prediction tasks.

• Transfer learning and generalization: Pre-training on heterogeneous, multi-theory datasets enables rapid adaptation to new chemical spaces, levels of theory, and even distinct physical contexts (e.g., catalysis, battery migration barriers) with minimal fine-tuning (Chen et al., 18 Sep 2024, Bheemaguli et al., 3 Dec 2025, Allen et al., 2023). Joint or cotraining strategies with replay and domain metadata (spin state, fidelity) are indispensable to avoid catastrophic forgetting and to handle mixed-physics data (Allam et al., 27 Oct 2025).
• Multi-task and multi-level learning: Training on multi-modal labels (quantum, biological) spanning up to 3,000 supervised properties for 100M molecules yields GNN backbones whose representations encode both quantum chemistry and functional bioactivity, facilitating low-resource transfer (Beaini et al., 2023).
• Uncertainty quantification (UQ): Ensemble-based, Bayesian, or misspecification-aware (POPS-hypercube) techniques are employed to quantify uncertainties from model misspecification—propagating realistic error bars to derived observables, including structure, defect formation energies, and phase stability (Perez et al., 10 Feb 2025).

5. Acceleration of Atomistic Simulation Workflows and Benchmark Performance

Foundational MLPs achieve significant speedups (often $10^5$-$10^6\times$ over DFT), making large-scale and long-timescale MD feasible with accuracy approaching that of the underlying quantum reference.

• Molecular and materials simulation: Large-scale MD (crystals, liquids, surfaces, high-entropy alloys) is supported with Pareto-optimal models balancing accuracy ($<20$ meV/atom for formation energies) and inference time (e.g., GRACE: 91 $\mu$s/atom/step on A100 GPU for F1=0.890 on MatBench) (Lysogorskiy et al., 25 Aug 2025).
• Phases and transitions: Incorporating differentiable trajectory reweighting (DiffTRe), foundation models are fine-tuned directly against experimental phase transition temperatures and pressures, correcting systematic biases present in DFT-trained potentials and enabling chemical-accuracy phase diagrams (Fuchs et al., 3 Dec 2025).
• Ionic migration and reaction pathways: MACE, Orb-v3, SevenNet deliver $E_m$ barrier MAEs of $<0.3$ eV in battery-relevant compounds, classify conductors vs. nonconductors at $>82\%$ accuracy, and provide relaxed NEB images superior to linear interpolation in $>70\%$ of cases (Bheemaguli et al., 3 Dec 2025).
• Generalization across chemical space: Meta-trained ANI and AIO-ANI architectures show robust data efficiency (4–10$\times$ fewer data needed for downstream adaptation) and smoothness of the inferred PES—even in transfer to molecular systems or chemical accuracy generalization on GMTKN55 tasks (Allen et al., 2023, Chen et al., 18 Sep 2024).

6. Limitations, Open Challenges, and Prospective Directions

Although foundational MLPs significantly advance the state of atomistic simulation, several open challenges remain:

• Long-range interactions and global effects: Existing models address long-range electrostatics, spin, and charge transfer either through explicit corrections (Ewald/k-space summations, dynamical charge equilibration), hybrid schemes, or global embedding; many-body dispersion and excited-state properties require further integration (Kocer et al., 2021, Fabritiis, 17 Aug 2024).
• Data and computational scaling: Training at the foundational scale requires petascale computational resources and large, standardized datasets; efficient distillation and hardware/algorithm co-design (specialized ML-MD accelerators) are emerging solutions (Yuan et al., 13 Mar 2025).
• Misspecification and validation: Error envelopes and UQ for misspecified models are essential for trust in deployment and automated discovery; robust, multi-fidelity, misspecification-aware schemes mitigate overfitting and excessive optimism in predicted observables (Perez et al., 10 Feb 2025).
• Multi-species and compositional generalization: Scaling descriptors and representations to handle full periodic table coverage without exponentially increasing parameter count remains an active area of research; approaches include channel-encoded local frames and latent chemical embeddings (Lysogorskiy et al., 25 Aug 2025).
• Integration of structure and knowledge: The next stage of “reasoning” in MLPs may require explicit encoding of causal structure, logical constraints, or graph-level semantics, further narrowing the effective hypothesis space and enhancing OOD robustness (Zhang et al., 2022).

7. Outlook: Standardization, Community Resources, and Impact

The rise of foundational MLPs—accompanied by public datasets (OMat24, OC20, ANI, Alexandria, Mixes), open-source model repositories (MACE, AIO-ANI, GRACE, Graphium), and standardized benchmarking protocols—signals a convergence toward universal, inference-efficient, and uncertainty-aware interatomic potentials (Lysogorskiy et al., 25 Aug 2025, Beaini et al., 2023). These models are catalyzing discovery across chemistry and materials science, enabling rapid simulation, screening, and design at scale, and lowering the barrier to integrating advanced machine learning into atomistic, mesoscale, and multiscale workflows.

Continued development of foundational MLPs will hinge on community-wide collaboration—amassing diverse, high-quality training data; transparent evaluation on OOD and dynamics; and methodological cross-pollination from statistical learning theory, computational physics, and applied machine learning (Yuan et al., 13 Mar 2025). The ultimate objective is routine, reliable, and first-principles-accurate simulation for scientific and technological innovation across the molecular and materials sciences.