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arxiv: 2503.10471 · v2 · submitted 2025-03-13 · ❄️ cond-mat.mtrl-sci · cs.AI

Siamese Foundation Models for Crystal Structure Prediction

Liming Wu , Wenbing Huang , Rui Jiao , Jianxing Huang , Liwei Liu , Yipeng Zhou , Hao Sun , Yang Liu
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Fuchun Sun Yuxiang Ren Jirong Wen
This is my paper

Pith reviewed 2026-05-23 00:08 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci cs.AI
keywords crystal structure predictiondiffusion modelsSiamese foundation modelsmaterials discoveryenergy predictionsuperconductorsstructure generation
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The pith

Pretrained Siamese foundation models generate crystal structures from composition that match experiments at 100 percent with 0.0012 atomic-position error while running over 2000 times faster than DFT.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents DAO as a pretrain-finetune framework that pairs a diffusion-based structure generator with an energy predictor, both built as Siamese foundation models. The generator is pretrained on large collections of stable and unstable structures, with the predictor used to relax unstable outputs during sampling. This combination improves results on standard benchmarks across multiple architectures and delivers exact experimental matches on three real superconductors. A reader would care because conventional DFT-based prediction is too slow for broad materials exploration, so a fast, generalizable alternative could expand the set of testable compositions.

Core claim

DAO integrates a diffusion-based structure generator and an energy predictor as Siamese foundation models. The generator is pretrained via a two-stage pipeline on a vast dataset of stable and unstable structures, with the predictor relaxing unstable configurations to guide generative sampling. Across benchmarks pretraining boosts performance on multiple backbones, and ablation studies confirm mutual benefit between the two models. On the real superconductor Cr6Os2 the method reaches 100 percent match with experimental references and 0.0012 atomic-position error under 20-shot generation, more than 2000 times faster per iteration than DFT-based predictors.

What carries the argument

The DAO framework of Siamese diffusion generator and energy predictor, where the predictor relaxes unstable structures to steer generative sampling.

If this is right

  • Pretraining on stable and unstable data improves prediction accuracy across multiple backbone architectures on standard benchmarks.
  • Ablation studies show the generator and predictor mutually reinforce each other.
  • The same models reach 100 percent experimental match rate and 0.0012 position error on Cr6Os2 and comparable results on two other superconductors.
  • Generation runs over 2000 times faster per iteration than DFT-based structure predictors.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The approach could be applied to screen far larger numbers of compositions for candidate materials before any DFT run.
  • If the predictor generalizes, it might replace some relaxation steps inside existing high-throughput workflows.
  • The same pretraining pattern could be tested on structure prediction tasks that involve temperature or external fields.
  • Failure on a held-out real material would indicate the need for larger or more diverse pretraining sets.

Load-bearing premise

Models pretrained on the collection of stable and unstable structures will generalize accurately to real-world materials outside the training distribution.

What would settle it

A new composition whose experimentally determined structure differs substantially from any structure generated by the pretrained DAO model under the reported sampling protocol.

Figures

Figures reproduced from arXiv: 2503.10471 by Fuchun Sun, Hao Sun, Jianxing Huang, Jirong Wen, Liming Wu, Liwei Liu, Rui Jiao, Wenbing Huang, Yang Liu, Yipeng Zhou, Yuxiang Ren.

Figure 1
Figure 1. Figure 1: A summary of our models: (a) offers an overview of the structure generator (DAO-G) and the energy predictor (DAO-P). (a.1) outlines the pretrain-finetune framework. DAO-G conducts a two-stage pretraining process on CrysDB and DAO-P is pretrained on the same dataset. DAO-P enhances DAO-G by dataset relaxation and energy guidance. (a.2) illustrates the pretraining of DAO-P, which involves the diffusion-based… view at source ↗
Figure 2
Figure 2. Figure 2: Statistics of the pretraining dataset CrysDB: (a) shows the global analyses of the dataset, including the number of entries from MP and OQMD, the statistics of the deduplicated version, and the propotion of stable structures. (b) reports the distributions of Ehull, volume and atom number. (c) presents the elements coverage. It is important to note that the statistics presented in (b) and (c) refer to the d… view at source ↗
Figure 3
Figure 3. Figure 3: In-depth analyses of our models on the CSP benchmarks: (a) compares the performance of DAO-G across various configurations. Here, “stage I, Stable” refers to pretraining on the stable-only subset of the deduplicated CrysDB, while “stage I” denotes the first-stage pretraining on the full deduplicated CrysDB. (b) gathers the polymorphs (with 2 to 4 conformations) from MP-20, and subsequently compares the gen… view at source ↗
Figure 4
Figure 4. Figure 4: The performance of DAO-P for crystal property prediction is evaluated on eight datasets. The compared baselines include models both with and without pretraining, with the results directly taken from their respective papers. For baselines where the corresponding experiments were not conducted in the original paper, the results are denoted as N/A. significant energy reduction of 86.8%, decreasing from 0.3198… view at source ↗
Figure 5
Figure 5. Figure 5: Experiments on superconductors: (a) depicts the finetuning process of DAO-P and DAO-G on the SuperCon3D dataset [11], in which 3D structures are known for a subset of materials. (b) presents the distributions of the critical temperature (Tc). (c) displays the Tc prediction error evaluated with the 5-fold cross-validation setting. (d) shows the results of the three recently discovered real-world superconduc… view at source ↗
Figure 6
Figure 6. Figure 6: An illustration of the structure relaxed by DFT and the structure generated by DAO-G, for the superconductor CsV3Sb5 [23]. fractional coordinates deviation. Only four out of ten runs of CsV3Sb5 [23] succeeds, with the best achieving an RMSE of 0.0637 compared to DAO-G’s 0.0085. The visualization results are depicted in [PITH_FULL_IMAGE:figures/full_fig_p030_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The illustration of energy guidance process. The blue arrow represents standard denoising based on the data distribution, which, however, not lies within stable regions. The brown arrow indicates the influence of energy guidance, steering the generation towards the equilibrium distribution. The resulting energy-guided denoising is depicted by the green arrow. 2.5 Pretraining Dataset Deduplication When pret… view at source ↗
Figure 8
Figure 8. Figure 8: Visualization of the generated structures by DAO-G throughout the diffusion process. We show representative structures at timesteps 1000, 750, 500, 250, and 0. The structures at timestep 0 represent the final generated samples, which are well-aligned with the corresponding ground truth structures. To enhance visual clarity and facilitate comparison, a common atom within each group (represented by a row) ha… view at source ↗
read the original abstract

Predicting crystal structures from chemical compositions is a fundamental challenge in materials discovery, complicated by complex 3D geometries that distinguish it from fields like protein folding. Here, we present Diffusion-based Crystal Omni (DAO), a pretrain-finetune framework for crystal structure prediction integrating two Siamese foundation models: a structure generator and an energy predictor. The generator is pretrained via a two-stage pipeline on a vast dataset of stable and unstable structures, leveraging the predictor to relax unstable configurations and guide the generative sampling. Across two well-known benchmarks, pretraining significantly enhances performance across multiple backbone architectures. Ablation studies confirm that the synergy between the generator and predictor mutually benefits both components. We further validate DAO on three real-world superconductors ($\text{Cr}_6\text{Os}_2$, $\text{Zr}_{16}\text{Rh}_8\text{O}_4$, and $\text{Zr}_{16}\text{Pd}_8\text{O}_4$) typically inaccessible to conventional computation. For $\text{Cr}_6\text{Os}_2$, DAO achieves a 100\% match rate with experimental references and an atomic-position error of 0.0012 under 20-shot generation, performing over 2000$\times$ faster per iteration than DFT-based structure predictors. These compelling results collectively highlight the potential of our approach for advancing materials science research.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript presents Diffusion-based Crystal Omni (DAO), a pretrain-finetune framework that integrates two Siamese foundation models—a structure generator pretrained via a two-stage pipeline on stable and unstable structures and an energy predictor used to relax unstable configurations during generative sampling. The paper claims that pretraining enhances performance across multiple backbone architectures on two benchmarks, that ablation studies confirm mutual benefits between generator and predictor, and that the approach achieves 100% match rate with experimental references and 0.0012 atomic-position error for Cr6Os2 (plus results on two Zr-based superconductors) under 20-shot generation while being over 2000× faster per iteration than DFT-based predictors.

Significance. If the generalization claims hold, the work could meaningfully accelerate materials discovery for complex compositions by replacing expensive DFT relaxations with fast learned sampling and relaxation. The two-stage pretraining on both stable and unstable structures plus the Siamese predictor-generator coupling is a concrete technical idea whose value would be established by the reported benchmark gains and real-world matches.

major comments (2)
  1. [Results on real-world validation] Results section on real-world superconductors: the 100% match rate and 0.0012 position error for Cr6Os2 under 20-shot generation is offered as evidence that the framework works on materials “typically inaccessible to conventional computation,” yet no overlap statistics between the three test compositions and the pretraining distribution, no leave-one-family-out protocol, and no analysis of predictor behavior on out-of-manifold proposals are supplied; without these the numerical result cannot confirm the claimed extrapolation.
  2. [Methods on pretraining pipeline] Methods on the two-stage pretraining pipeline: the claim that the predictor “guides the generative sampling” by relaxing unstable configurations is central to the synergy argument, but the manuscript provides no quantitative characterization (e.g., predictor error distribution or success rate) of how the predictor behaves when the generator proposes structures far from the pretraining manifold.
minor comments (2)
  1. [Abstract] Abstract: the two “well-known benchmarks” are never named; this information should appear in the first paragraph of the results or methods.
  2. [Abstract] Abstract and methods: dataset sizes, exact model architectures, and training hyperparameters are omitted, which impedes immediate assessment of reproducibility even if the central claims are later supported.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below and indicate where revisions will be made.

read point-by-point responses

  1. Referee: [Results on real-world validation] Results section on real-world superconductors: the 100% match rate and 0.0012 position error for Cr6Os2 under 20-shot generation is offered as evidence that the framework works on materials “typically inaccessible to conventional computation,” yet no overlap statistics between the three test compositions and the pretraining distribution, no leave-one-family-out protocol, and no analysis of predictor behavior on out-of-manifold proposals are supplied; without these the numerical result cannot confirm the claimed extrapolation.

    Authors: We agree that overlap statistics would better contextualize the results. In the revised manuscript we will add compositional similarity metrics (e.g., element-frequency overlap and space-group distribution) between Cr6Os2, Zr16Rh8O4, Zr16Pd8O4 and the pretraining set. A full leave-one-family-out protocol is not part of the standard benchmarks used in the field and would require new large-scale experiments; we will instead expand the discussion of chemical-family membership. For predictor behavior on out-of-manifold proposals, the two-stage pretraining on unstable structures is intended to improve robustness; we will add a quantitative error-distribution analysis on the generated real-world samples. revision: partial

  2. Referee: [Methods on pretraining pipeline] Methods on the two-stage pretraining pipeline: the claim that the predictor “guides the generative sampling” by relaxing unstable configurations is central to the synergy argument, but the manuscript provides no quantitative characterization (e.g., predictor error distribution or success rate) of how the predictor behaves when the generator proposes structures far from the pretraining manifold.

    Authors: We accept that additional quantitative detail is needed. The revised methods section will report the predictor’s error distribution and relaxation success rate on structures proposed by the generator during sampling, including cases distant from the pretraining manifold, using statistics collected from the ablation experiments already performed. revision: yes

Circularity Check

0 steps flagged

No circularity; empirical results on external benchmarks

full rationale

The paper describes a pretrain-finetune ML framework evaluated on standard benchmarks and three external experimental compositions (Cr6Os2 etc.). No equations, derivations, or first-principles steps are presented that reduce claimed performance metrics to fitted parameters or self-referential definitions by construction. Ablation studies and match-rate numbers are reported against held-out or real-world references, keeping the derivation chain independent of its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated. The framework implicitly relies on standard assumptions of diffusion models and energy predictors but these are not detailed.

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