ATLAS: A Foundation Neural Sampler for Amorphous Materials

Detailed Research Summary: ATLAS - A Foundation Neural Sampler for Amorphous Materials

This research introduces ATLAS (Amorphous Transition Learning and Sampling System), a novel foundation model designed to address the significant computational challenges associated with sampling and designing amorphous materials. Amorphous materials possess exceptional mechanical and functional properties, but their rugged energy landscapes make conventional molecular dynamics (MD) and Monte Carlo (MC) methods inefficient due to the need for rare barrier-crossing events during equilibration. Furthermore, existing data-driven generative models are often constrained by scarce or biased reference ensembles. ATLAS is presented as an efficient sampler that learns a diffusion process to generate Boltzmann-distributed amorphous structures directly from a target potential energy function, establishing itself as a unified framework for sampling, steering, and designing disordered systems.

Core Methodology and Architecture

The central innovation of ATLAS lies in its ability to learn the underlying stochastic dynamics of amorphous systems. The model is parameterized by an equivariant Graph Neural Network (GNN). A key methodological feature is that the GNN is trained on bootstrapped configurations generated by ATLAS itself. This self-training allows the network to recover both the forward and backward stochastic dynamics, utilizing the target potential energy U(x) as direct supervision rather than relying on pre-existing reference structures.

ATLAS learns to transform a uniform prior under periodic boundary conditions into a true Boltzmann distribution (proportional to [-beta U(x)]) through this learned diffusion process. Crucially, the model is designed to be highly generalizable, capable of operating across variations in system size, temperature, and chemical composition. This generalization capability is further enhanced by a composition-amortized pretraining strategy, which significantly reduces the cost associated with training specific models for different compositions compared to training from scratch.

Capabilities: Sampling and Thermodynamic Estimation

Once trained, ATLAS provides a suite of powerful downstream capabilities rooted in its learned diffusion process:

1. Thermodynamic Property Estimation: The learned forward and backward path likelihood ratios allow for the efficient estimation of temperature-dependent quantities such as the partition function Z(T), free energy F(T), and entropy S(T).

2. Ensemble Sampling: Independently generated configurations from ATLAS provide accurate ensemble estimates of structural and thermodynamic observables under the target Boltzmann distribution.

3. Inference-Time Steering (Control): ATLAS enables efficient exploration of rare regions in configuration space by allowing for inference-time steering toward specific targets. This is achieved through reward tilting: given a pretrained base distribution p base(x) proportional to [-beta U(x)], the distribution can be tilted to p eta(x) = Z-1 p base(x) [eta r(x)], where r(x) is a user-defined reward function and eta controls the tilt strength.

4. Potential of Mean Force (PMF) Recovery: Inference-time steering can efficiently explore rare regions to recover the PMF, F(xi), along prescribed collective variables xi.

Applications in Materials Science: From Sampling to Design

ATLAS is not merely a sampling tool; it functions as a foundation model enabling complex material design tasks:

• Structural Conditioning: ATLAS can be used as a conditional generator on expectation values. For instance, Short-Range Order (SRO) conditioning using the Warren-Cowley parameter alpha ij is demonstrated by applying a reward function r(x) = -[alpha ij(x) - alpha* ij] squared to systematically shift generated ensembles toward prescribed SRO values.

• Property-Guided Generation: To steer structures toward specific macroscopic properties, such as a higher bulk modulus, ATLAS utilizes a differentiable surrogate model (x) (approximating the true property calculation) as the terminal reward: r(x) = (x). This strategy systematically shifts generated ensembles toward desired mechanical stiffness.

• Inverse Design via Agentic Optimization: The ultimate demonstration of ATLAS's power is its coupling with an agentic Large Language Model (LLM) and a universal Machine Learning Interatomic Potential (MLIP, specifically MACE-MPA-0). In the context of high-entropy metallic glasses, the LLM agent iteratively proposes new compositions based on ensemble properties evaluated by ATLAS. This coupled system searches an eight-element compositional space to identify a converged Pareto frontier balancing competing objectives like stiffness and ductility, achieving this identification within a remarkably small number of oracle evaluations (480).

Significance and Future Outlook

ATLAS establishes a paradigm shift by unifying thermodynamic prediction, inverse structural inference, controllable generation, and composition-level inverse design into a single computational framework. The paper asserts that the same principles—direct ensemble sampling, controllable generation via reward tilting, and agentic optimization—can be applied to other disordered systems such as oxide glasses and polymers by simply incorporating different constraints.

In essence, ATLAS provides a foundation model for amorphous materials, transforming the traditionally difficult problem of sampling rugged energy landscapes into a tractable query within a unified generative model. This framework promises scalable inverse design in complex disordered materials by replacing repeated, expensive trajectory generation with an amortized and controllable sampler.

1. AI systems can directly sample Boltzmann-weighted structural ensembles from a target energy function, as ATLAS learns a diffusion process to generate Boltzmann-distributed amorphous structures directly from a target energy function. This allows for the generation of independent amorphous configurations together with free energy estimates and Boltzmann-weighted observables without relying on biased reference datasets.

2. AI systems can perform efficient thermodynamic estimation by exploiting the time reversal of the diffusion process, enabling efficient estimation of thermodynamic quantities and steering toward target observables, such as recovering free energy and entropy with below 0.2% free energy error in the low-temperature glass regime with over 500-fold fewer energy evaluations.

3. AI systems can steer generated structures toward specific physical properties by implementing reward tilting, such as conditioning on short-range order (SRO) or mechanical moduli, as demonstrated by steering structures toward prescribed order parameters and optimized bulk moduli. This capability allows for observable-guided generation where the model is updated so that generated samples have increased probability under pη.

4. AI systems can enable complex materials inverse design via an agentic framework, where ATLAS acts as a foundation model for sampling, steering and designing amorphous materials, coupled with an LLM-guided evolutionary algorithm to search eight-element spaces for high-entropy metallic glasses balancing stiffness and ductility. This system can identify a converged Pareto frontier within 480 oracle evaluations.

5. AI systems can be amortized across chemical composition space, allowing a single composition-conditioned ATLAS model to generate ensembles for various alloys and reuse it, reducing training costs by several hundred-fold compared to training composition-specific models from scratch. This amortization enables repeated queries without retraining throughout the search.