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.
We present a variational functional neural network (vfNN) algorithm that optimizes physically motivated continuum functionals in integral form (e.g., Lagrangian, Hamiltonian, or free energy) to find the states of a system. That way, vfNN bypasses solving the equations of motion (a.k.a. the Euler-Lagrange equations), which are in the form of differential equations. To this end, our approach is fundamentally different from conventional physics-informed neural networks (PINN) that solve differential equations by minimizing a phenomenological loss function involving higher order derivatives and ad hoc weight factors. In contrast, vfNN merely evaluates lower order derivatives of the generating functional and replaces the weight factors with rigorous physical scales. This also fundamentally changes the loss landscape, and the desired solutions may become unstable. For this emergent nonconvex optimization problem, we develop a quasi-Newton optimization algorithm with simulated annealing that converges to the solutions of the corresponding Euler-Lagrange equations of the functional regardless of their stability properties. Our simulations using vfNN give accurate results for benchmark systems governed by linear or nonlinear ordinary differential equations.
Machine learning for chemical vapor deposition (CVD) of carbon nanotubes (CNTs) has largely mapped static synthesis conditions to final properties, implicitly treating these conditions as a complete description of growth. Here, we test this assumption by integrating gas-flow conditions with in-situ time-resolve growth profiles (growth curves) of vertically aligned CNT forests. We introduce an observation-window analysis, in which prediction is evaluated as a function of observation time by providing models with the growth curve only up to progressively later times, to determine not only whether a property can be predicted, but when the necessary information becomes available during synthesis. Clustering of normalized growth curves revealed distinct growth patterns independent of final forest height. The gas conditions alone could predict the initial growth rate but not the growth lifetime and failed to capture the variation in yield (R^2<0). Adding the growth curve improved yield prediction (R^2~0.4-0.5), with the relevant information emerging during the intermediate and later stages of growth rather than at its onset. In contrast, density and G/D ratio, which forest height does not record, showed no consistent improvement. The maximum height and lifetime could be estimated with moderate accuracy midway through the 10-min growth. Permutation feature importance identified water vapor and H_2, both linked to catalyst activity, as the most informative gas variables. These results indicate that variation unexplained by synthesis conditions is not merely noise but reflects an evolving catalyst state, and they establish mid-growth decision points for autonomous synthesis, enabling early termination of unpromising batches and, ultimately, in-batch adjustment of growth conditions.
Using machine learning, we identify a second transition in polymer chain stretching driven by planar elongational flow, beyond the well-known coil-stretch transition. We achieve this by developing a conditional extension of Universal and Identifiable Dissipative Dynamics (UIDD) that jointly learns reduced stochastic dynamics from microscopic trajectories across flow strengths and yields the corresponding stationary nonequilibrium free energy landscapes. As the flow strength increases, the evolving landscape exhibits the expected coil-stretch transition, and then a previously unrecognized dynamical transition. In the latter, the stretched states persist, but the distribution along a folding coordinate becomes bimodal when conditioned on small end-to-end separation. Large-deviation analysis of a simplified analytical chain model reproduces both transitions and shows that they are phase transitions in the long-chain limit. Single-molecule DNA experiments provide qualitative support for the dynamical transition through the predicted reversal of the folding response.
Accurately predicting the transport properties of liquid electrolytes is critical for next-generation battery design and requires force fields that are both quantum-mechanically accurate and fast enough for long-timescale simulation. Recent large-scale pretrained machine learning interatomic potentials (MLIPs) approach density-functional-theory accuracy, but remain too slow to access the necessary timescales to converge transport properties. We provide a knowledge distillation procedure to transfer the accuracy of a large-scale "teacher" MLIP into fast, system-specific "students", without any additional ab initio data. Our distilled models run ~40x faster, reproduce teacher-predicted structural observables, and produce stable 20 ns trajectories in days, rather than the months the teacher would require. Across a diverse set of sodium- and lithium-ion electrolytes, student-predicted self-diffusivities, ionic conductivities, and shear viscosities track experiment and outperform classical force-field predictions, establishing distillation as a practical route to accurate, long-timescale simulations necessary for high-throughput electrolyte screening.
Programming the static friction of mechanical interfaces is critical for soft robotics, haptics, and precision gripping. Static friction is governed by the real contact area, and standard rough surfaces exhibit a linear area-load scaling inherent to classical models, severely restricting their functional range. Here, we propose a framework for the inverse design of tribological metainterfaces engineered for programmable contact behaviors. By utilizing general axisymmetric asperities, we unlock nonlinear macroscopic responses unattainable by standard Hertzian contacts. To solve the inverse problem, we embed a fully differentiable contact mechanics engine within a neural network and a quadratic optimizer. We leverage regularized physical gradients to automatically discover non-standard topographies that reproduce complex target contact laws, with only a few asperities in unit cells. The predicted designs are validated against high-fidelity Boundary Element Method (BEM) simulations. By front-loading computational costs during training, the neural surrogate yields near-instantaneous design inference, bypassing the bottlenecks of traditional multi-start optimization. This framework bridges data-driven optimization and rigorous physics, offering a scale-invariant pathway for the high-throughput discovery and real-time control of functional tribological surfaces.