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Offline Materials Optimization with CliqueFlowmer

NeurIPS 2026 · Probabilistic and scientific modeling › Molecules and proteins · approach: Machine-learned interatomic potentials · 0 citations (OpenAlex)

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Proposes CliqueFlowmer, a transformer autoencoder with clique-structured latent space, trained jointly with a property predictor, that optimizes materials offline via evolution-strategies gradient search and decodes them with an autoregressive atom-type decoder and flow-matching geometry decoder.

Problem

Generative models for computational materials discovery mainly reproduce the training distribution and do not actively optimize a target property; offline model-based optimization is hard for irregular, hybrid discrete-continuous materials structures.

Approach

Encode materials into a fixed-dimensional latent with a transformer encoder, impose a clique-chain decomposition on the latent for the property predictor, optimize latents with rank-based evolution strategies plus weight decay, and decode back to atom types (autoregressive + beam search) and geometry (conditional flow matching).

Key results

• Optimized formation energy per atom reaches -0.81 (CliqueFlowmer) and -0.99 (CliqueFlowmer-Top) vs. 0.59-0.71 for generative baselines.
• Band gap reduced to 0.03 (CliqueFlowmer) and 0.07 (-Top) vs. 0.48-0.63 for baselines, with S.U.N. 61.3% and 69.4%.
• Under DFT re-evaluation on 100 structures, S.U.N. rates drop sharply (e.g., 2% strictly S.U.N. for CliqueFlowmer), showing sensitivity to ML oracle bias.

Surprising findings

• Under DFT evaluation the S.U.N. rates of CliqueFlowmer fall far below the ML-oracle estimates, while property optimization advantage persists.
• Backpropagation through the property predictor diverges; rank-based evolution strategies with weight decay work instead.

Limitations

• Property oracles are ML surrogates (M3GNet, MEGNet) and formation energy/band gap are synthetic targets; stability metrics are sensitive to oracle bias.
• Stability and S.U.N. evaluated with approximate M3GNet relaxation; DFT check limited to 100 structures.
• Lower stable and metastable rates for formation-energy optimization (e.g., 14.5% stable vs. 19.8% for DiffCSP++).

Experimental setup

Datasets: MP-20

Benchmarks: MP-20

Metrics: formation energy per atom (M3GNet) band gap (MEGNet) stability (energy above hull) S.U.N. rate metastable rate novelty uniqueness DFT formation energy and band gap (HSE)

Baselines: CrystalFormer DiffCSP DiffCSP++ MatterGen

Builds on: Cliqueformer flow matching AdaLN Cliqueformer clique decomposition AdamW

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