# Proof-Carrying Materials: Falsifiable Safety Certificates for Machine-Learned Interatomic Potentials

arXiv: https://arxiv.org/abs/2603.12183 · HTML: https://mlsanity.com/paper/2603.12183/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 68 references that are in the map.
- First posted on arXiv 12 Mar 2026.

## Builds on (most cited first, 24 of 24)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition](https://mlsanity.com/paper/2504.21801/) (2025)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representations](https://mlsanity.com/paper/2306.12059/) (2023)
- [Towards Guaranteed Safe AI: A Framework for Ensuring Robust and Reliable AI Systems](https://mlsanity.com/paper/2405.06624/) (2024)
- [14 Examples of How LLMs Can Transform Materials Science and Chemistry: A Reflection on a Large Language Model Hackathon](https://mlsanity.com/paper/2306.06283/) (2023)
- [Less is more: sampling chemical space with active learning](https://mlsanity.com/paper/1801.09319/) (2018)
- [Uncertainty Quantification Using Neural Networks for Molecular Property Prediction](https://mlsanity.com/paper/2005.10036/) (2020)
- [Guidance on the Assurance of Machine Learning in Autonomous Systems (AMLAS)](https://mlsanity.com/paper/2102.01564/) (2021)
- [Are LLMs Ready for Real-World Materials Discovery?](https://mlsanity.com/paper/2402.05200/) (2024)
- [Matbench Discovery -- A framework to evaluate machine learning crystal stability predictions](https://mlsanity.com/paper/2308.14920/) (2023)
- [Compositional Falsification of Cyber-Physical Systems with Machine Learning Components](https://mlsanity.com/paper/1703.00978/) (2017)
- [LLM-Prop: Predicting Physical And Electronic Properties Of Crystalline Solids From Their Text Descriptions](https://mlsanity.com/paper/2310.14029/) (2023)
- [A practical guide to machine learning interatomic potentials -- Status and future](https://mlsanity.com/paper/2503.09814/) (2025)
- [Committee neural network potentials control generalization errors and enable active learning](https://mlsanity.com/paper/2006.01541/) (2020)
- [Learning atomic forces from uncertainty-calibrated adversarial attacks](https://mlsanity.com/paper/2502.18314/) (2025)
- [Proof-Carrying Neuro-Symbolic Code](https://mlsanity.com/paper/2504.12031/) (2025)

## Built on by (most cited first, 1 of 1)

- [MLIP Detective: Active Failure Mode Discovery Beyond Benchmark Scores for Machine-Learning Interatomic Potentials](https://mlsanity.com/paper/2609.08399/) (2026)

## Abstract (arXiv)

Machine-learned interatomic potentials (MLIPs) are deployed for high-throughput materials screening without formal reliability guarantees. We show that a single MLIP used as a stability filter misses 93% of density functional theory (DFT)-stable materials (recall 0.07) on a 25,000-material benchmark. Proof-Carrying Materials (PCM) closes this gap through three stages: adversarial falsification across compositional space, bootstrap envelope refinement with 95% confidence intervals, and Lean 4 formal certification. Auditing CHGNet, TensorNet and MACE reveals architecture-specific blind spots with near-zero pairwise error correlations (r <= 0.13; n = 5,000), confirmed by independent Quantum ESPRESSO validation (20/20 converged; median DFT/CHGNet force ratio 12x). A risk model trained on PCM-discovered features predicts failures on unseen materials (AUC-ROC = 0.938 +/- 0.004) and transfers across architectures (cross-MLIP AUC-ROC ~ 0.70; feature importance r = 0.877). In a thermoelectric screening case study, PCM-audited protocols discover 62 additional stable materials missed by single-MLIP screening - a 25% improvement in discovery yield.