AMShortcut: An Inference- and Training-Efficient Inverse Design Model for Amorphous Materials

Amorphous (disordered) materials are solids that have shown great potential in various domains, including energy storage, thermal management, and advanced materials. Unlike crystalline materials that can be described by unit cells containing a few to hundreds of atoms, amorphous materials require larger simulation cells with at least hundreds to thousands of atoms. To advance the design of amorphous materials with desired properties and facilitate the exploration of their vast design space, generative inverse design has emerged as a promising approach. It aims to directly output materials with properties closely aligned with the desired ones using probabilistic generative models conditioned on desired properties, which can be more resource efficient than the traditional trial-and-error approach. However, due to the inherent stochasticity of probabilistic generative models, when element assignments are unconstrained, a large portion of generated materials may be charge unbalanced, and no existing methods can effectively mitigate this limitation. In this work, we propose AMGenC, a new generative inverse design method for amorphous materials that can guarantee the generation of charge balanced samples, with minimal additional computational overhead and without sacrificing inverse design accuracy. AMGenC achieves this through an element noise that gives the generation process a starting point centered around charge balance, and the combination of a per-step soft projection and a final discrete projection for steering the elements toward exact charge balance throughout the generation. We perform extensive experiments on two amorphous materials datasets. Experimental results provide evidence that AMGenC achieves its design goal.

Amorphous materials exhibit exceptional mechanical and functional properties, yet their rugged energy landscapes are notoriously difficult to sample. Below the glass-transition temperature, conventional molecular dynamics and Monte Carlo become inefficient because equilibration relies on rare barrier-crossing events, while data-driven generative models are constrained by scarce and biased reference ensembles. Here, we introduce ATLAS, an efficient sampler that learns a diffusion process to generate Boltzmann-distributed amorphous structures directly from a target energy function. Parameterized by an equivariant graph neural network, ATLAS generalizes across system size, temperature, and composition. By exploiting the time reversal of the diffusion process, it enables efficient estimation of thermodynamic quantities and steering toward target observables. In two-dimensional Kob-Andersen systems, ATLAS reproduces parallel tempering Markov chain Monte Carlo structural distributions, free energies and entropies, achieving below 0.2% free energy error in the low-temperature glass regime with over 500-fold fewer energy evaluations. In Cu-Zr and Cr-Co-Ni metallic glasses, ATLAS recovers experimentally observed short-range-order trends and steers structures toward prescribed order parameters and optimized bulk moduli. Moreover, composition-amortized pretraining outperforms composition-specific training from scratch, reduces inverse-design costs by several hundred-fold, and enables sampling with expensive universal machine learning interatomic potentials. Coupled to a large language model agent, ATLAS searches an eight-element space for high-entropy metallic glasses balancing stiffness and ductility, identifying a converged Pareto frontier within 480 oracle evaluations. Together, these results establish ATLAS as a foundation model for sampling, steering and designing amorphous materials.

Inverse materials design is shifting materials discovery from forward prediction to targeted proposal of candidates that satisfy objectives under physical constraints. Here, we review recent advances in generative crystal structure modeling, multimodal learning, and closed-loop design pipelines for crystalline solids. We survey how modern generators learn chemical-structural priors from large databases to enable controllable sampling of periodic structures, and compare leading model classes including variational autoencoders, normalizing flows, autoregressive formulations, and diffusion models. Particular attention is given to how feasibility constraints and physical priors are enforced across the workflow, through representation choices, training objectives, sampling-time guidance, and post-generation screening and relaxation. We also discuss how multimodal learning fuses diverse materials modalities, including crystal structures, thermodynamic, electronic information, microscopy, spectroscopy, processing context, and scientific text, to construct a more universal, transferable representation of chemical space. In addition, diverse inverse-design strategies are examined, particularly those that integrate conditional generation with latent optimization, Bayesian optimization, reinforcement learning, and active learning. Finally, we highlight recurring failure modes, such as surrogate exploitation, diversity collapse, distribution shift, and the stability-synthesizability gap, and outline discovery-grade evaluation practices based on staged reporting of validity, novelty, uniqueness, stability, and cost.