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Automatic differentiation has enabled rapid progress on continuous-variable mechanical design problems, but gradient-based optimization still struggles with discrete variables. The standard approach is to optimize using a continuous relaxation of the choices, then commit to the nearest discrete design at the end. Why this procedure selects unfavorable basins is poorly understood. Here, we introduce a practical, interpretable design problem inspired by origami, in which automatic differentiation is used to design shapes with a target functional behavior. Each origami sheet has a fixed geometry, and a bilevel optimization framework tunes which one of four discrete hinge types to place at each fold. Baseline gradient-based design settles into basins with a large discretization gap: relaxed optimization solves 97% of runs, but the final, discrete solutions succeed only half the time. We find that the gap can be relieved with a surprisingly simple modification. An initialization prior uniformly biased toward the stiff, flat hinge option boosts the final solve fraction from 49% to 69%. Applying the prior adds no additional compute and leaves the optimization process unchanged. Compared to the baseline, sheets produced with the prior have greater geometric compatibility and mechanical stiffness. Directly penalizing frustration and floppiness in the outer loss function produces an even greater improvement than the prior does, raising the solve fraction to 78% and indicating that these properties help distinguish the unfavorable basins. Our results demonstrate that loss landscapes for mechanical design can have physically meaningful basins that are not robust to discretization and cause solves to fail. Targeting these basins' physical signatures, even with just an initialization bias, helps avoid them.

Predicting the thermodynamic properties of an alloy requires sampling its configurations across many chemical conditions and recovering free energies on a common absolute scale. Markov chain Monte Carlo (MCMC) is the standard tool, but it requires separate simulations at different conditions, and auxiliary free-energy methods such as thermodynamic integration are used to place results on a common absolute scale. Modern discrete neural samplers typically use reverse KL divergence as the objective and can be mode-seeking or biased. We present Free energy Offering Generative Sampler (FrOGS), a hybrid discrete neural sampler that couples an autoregressive model to a continuous-time Markov chain (CTMC) to be trained jointly under a single shared loss. FrOGS draws i.i.d. configurations, returns an unbiased estimate of the partition function, and gives consistent estimates of thermodynamic observables. We train a single model across a wide range of chemical conditions to produce estimates on a common absolute free-energy scale. FrOGS matches exact finite-size results on the 2D Ising model and reference phase diagrams for AgPd and CuAu, without mode collapse. We additionally compare to SEGAL, a published autoregressive baseline, and find that only FrOGS recovers the stability range of the CuAu$_3$ phase.

The search for new crystalline materials spans an enormous compositional and structural space. Generating candidates in this space requires modeling the relationships between elemental composition, crystallographic symmetry, and crystal geometry. The space group specifies the crystal's symmetry and determines the admissible Wyckoff positions and geometric degrees of freedom; fixing it in advance prevents this global symmetry choice from being revised using information from evolving Wyckoff occupations and elemental composition. We introduce DynaCrys, the first framework for complete crystal generation in which the space group co-evolves with Wyckoff occupations and elements. We develop physics-informed space-group diffusion that explicitly incorporates crystallographic group-subgroup relations, and a legality-constrained stochastic decoder that jointly samples compatible space groups, Wyckoff occupations, and elements, followed by symmetry-constrained geometry generation. In large-scale evaluations on standard benchmarks, DynaCrys achieves state-of-the-art performance in symmetry-aware crystal generation while supporting fast sampling.

Machine learning interatomic potentials (MLIPs) are commonly trained and evaluated by their ability to reproduce first-principles energies and forces. Practical value, however, is often determined by downstream processes such as structural relaxation. Much of MLIP literature is motivated by the expectation that improving force accuracy will produce correspondingly better downstream behavior. Although this expectation is natural, it may not hold in practice due to model inaccuracies. Here, we demonstrate that force accuracy and relaxation accuracy can be driven in opposite directions. Starting from pretrained MLIPs, we differentiate through relaxation trajectories and optimize the the final structures. This intervention produces increases in force-prediction errors while substantially reducing structural errors. Importantly, this represents a trade-off between two aspects of physical fidelity: the learned forces become less faithful to first-principles forces, while the resulting relaxed structures become more faithful to first-principles predictions. Rather than observing a discrepancy between local quality and downstream performance, we demonstrate that this discrepancy can be induced through optimization. Our findings suggest that MLIPs need not be optimized as approximations of first-principles forces, but can instead learn task-specific vector fields that guide relaxation trajectories toward more accurate final structures. By propagating supervision through complete relaxation trajectories, our framework captures dependencies between successive predictions that are absent when structure--force pairs are treated independently. More broadly, these results demonstrate that conventional force metrics can provide an incomplete assessment of downstream performance and highlights the importance of evaluating scientific machine-learning models within computational workflows.

Grain growth during heat treatment strongly affects the microstructure of polycrystalline materials and, consequently, their mechanical properties. Although numerical methods such as front-tracking or front-capturing simulations can accurately describe grain growth, their high computational cost limits their use for long or non-isothermal thermal cycles. In previous work, grain growth was successfully predicted under isothermal conditions by treating grain size distributions as time series and forecasting their evolution using recurrent neural networks, allowing complete grain growth trajectories to be generated in seconds rather than through costly PDE-based simulations. In the present work, this forecasting framework is reformulated to handle non-isothermal conditions by explicitly incorporating thermal information into the model architecture. Grain size distributions are encoded using a convolutional neural network, thermal descriptors are embedded through a dedicated multilayer perceptron, and temporal evolution is predicted using a recurrent network. Instantaneous temperature and thermal rate are provided at each time step, allowing the model to adapt its predictions to changing thermal conditions. The framework is trained and evaluated on datasets generated from validated front-tracking simulations across a wide range of non-isothermal thermal paths. The results show that the thermally conditioned model accurately reproduces grain growth dynamics under complex thermal histories, achieving, in k-fold cross-validation over all simulations, mean relative errors of 2.99% (one-hour cycles) and 4.51% (four-hour cycles) with coefficients of determination exceeding 0.99, and mean relative errors between 1.91% and 14.66% on ten simulations following four unseen thermal histories of increasing complexity.

Structure property prediction is a classical task in machine learning, ranging from molecular activity and materials properties to local functional responses measured in microscopy. For image-based regression, two choices define the information available to the predictor: the size of the image neighborhood and the spatial resolution retained within it. A small neighborhood can omit relevant surrounding structure, whereas a large, finely sampled neighborhood can introduce redundant or irrelevant information. Here, we develop a framework for constructing spatial descriptors for prediction of local spectra and hysteresis loops. We benchmark regression models, use SHAP maps to examine their spatial attribution, and explore the effect of the patch size and compression to establish the relationship between predictive accuracy and descriptor dimensionality. We then use a genetic algorithm to optimize spatial partitions and the assignment of mean, minimum, and maximum pooling operations. Each retained region contributes an explicit measurement of the image, allowing the search to balance prediction error against the number of descriptor values. Cartesian and polar constructions provide complementary ways to organize this information. The resulting descriptors make it possible to examine where spatial detail is needed, where regional summaries are sufficient, and how these choices depend on the predictor and the measured response. The same approach can be used for molecules and solids once the genetic algorithm rules for these are established.