March 2026

History-dependent constitutive models serve as macroscopic closures for the aggregated effects of micromechanics. Their parameters are typically learned from experimental data. With a limited experimental budget, eliciting the full range of responses needed to characterize the constitutive relation can be difficult. As a result, the data can be well explained by a range of parameter choices, leading to parameter estimates that are uncertain or unreliable. To address this issue, we propose a Bayesian optimal experimental design framework to […]

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Connections between statistical mechanics and machine learning have repeatedly proven fruitful, providing insight into optimization, generalization, and representation learning. In this work, we follow this tradition by leveraging results from non-equilibrium thermodynamics to formalize curriculum learning in reinforcement learning (RL). In particular, we propose a geometric framework for RL by interpreting reward parameters as coordinates on a task manifold. We show that, by minimizing the excess thermodynamic work, optimal curricula correspond to geodesics in this task space. As […]

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Key Highlights – Flash floods kill more than 5,000 people every year, and unlike most weather events, they are notoriously resistant to prediction. They are too short-lived and too localised to be tracked the way river flows or temperatures are — which means the deep learning models now capable of forecasting most weather patterns have had very little useful data to work with when it comes to flash floods specifically. Google’s approach to fixing that is, to put […]

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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 […]

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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 […]

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In the previous two posts, we looked at why Mathematica and SymPy did not simplify sinh(arccosh(x)) to √(x² − 1) as one might expect. After understanding why sinh(arccosh(x)) doesn’t simplify nicely, it’s natural to ask why sin(arccos(x)) does simplify nicely. In this post I sketched a proof of several identities including sin(arccos(x)) = √(1 − x²) saying the identities could be proved geometrically. Let x be between 0 and 1. Construct right triangle with hypotenuse of length 1 […]

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Here’s what I think is happening: AI-assisted coding is exposing a divide among developers that was always there but maybe less visible. Before AI, both camps were doing the same thing every day. Writing code by hand. Using the same editors, the same languages, the same pull request workflows. The craft-lovers and the make-it-go people sat next to each other, shipped the same products, looked indistinguishable. The motivation behind the work was invisible because the process was identical. […]

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