Friction on Demand: A Generative Framework for the Inverse Design of Metainterfaces

TL;DR

This work tackles the inverse design of frictional metainterfaces, a problem made challenging by non-uniqueness and expensive forward tribology simulations. It introduces a conditional variational autoencoder (CVAE) trained on a massive synthetic dataset to map target friction laws $\bm{F}(P)$ to surface topography parameters $\bm{\theta}$ described by a 4-component Gaussian Mixture Model, enabling near real-time generation of candidate topographies. The results show strong parameter-level accuracy ($\text{median } sMAPE \approx 2.27\%$, $\text{Adjusted } R^2 \approx 0.999$) but reveal a notable gap to end-to-end functional fidelity (CVAE mean $sMAPE$ around $37.95\%$) compared with a VAE plus CMA-ES optimizer, which achieves much lower functional error at the cost of substantial computation time. The study discusses the speed-accuracy trade-off, the sim-to-real gap, and practical use cases where rapid but approximate designs, or hybrid optimization workflows, can enable near-real-time control of friction through tailored surface topographies, with implications for broader scientific inverse design practices. $F(P)$, $\bm{\theta}$, and related quantities are expressed in mathematical form to reflect the governing relationships.

Abstract

Designing frictional interfaces to exhibit prescribed macroscopic behavior is a challenging inverse problem, made difficult by the non-uniqueness of solutions and the computational cost of contact simulations. Traditional approaches rely on heuristic search over low-dimensional parameterizations, which limits their applicability to more complex or nonlinear friction laws. We introduce a generative modeling framework using Variational Autoencoders (VAEs) to infer surface topographies from target friction laws. Trained on a synthetic dataset composed of 200 million samples constructed from a parameterized contact mechanics model, the proposed method enables efficient, simulation-free generation of candidate topographies. We examine the potential and limitations of generative modeling for this inverse design task, focusing on balancing accuracy, throughput, and diversity in the generated solutions. Our results highlight trade-offs and outline practical considerations when balancing these objectives. This approach paves the way for near-real-time control of frictional behavior through tailored surface topographies.

Figures (14)

• Figure 1: Representative surface topographies generated by the CVAE from three distinct latent samples for the same target, demonstrating the model's ability to capture the multimodality of the solution space.
• Figure 2: Comparison of sMAPE error distributions. (\ref{['fig:dist-vae']}) Distribution for the VAE + CMA-ES method over 225 randomly selected test samples. Mean error and 99% confidence interval are shown by the dashed red line and shaded region. The x-axis is broken to show the full range of data. (\ref{['fig:dist-cvae']}) Error distribution for the CVAE. Mean error and 95% confidence interval, estimated via 1,000 bootstrap resamples, are shown by the dashed red line and shaded region.
• Figure 3: CVAE sMAPE performance across different physical regimes, defined by the number of asperities (x-axis) and the mean friction force (y-axis).
• Figure 4: Comparison of friction laws generated by the VAE + CMA-ES and the CVAE models against the experimental friction law target (solid black line) and its GMM approximation (dotted green line). The result from the best-performing of 100 VAE + CMA-ES optimization runs is shown as a red dashed line. The surrounding pink shaded area represents the model uncertainty, quantified as one standard deviation across all 100 runs. For the CVAE, the blue dash-dotted line is the mean prediction over 100,000 inferences, with the light blue area indicating the corresponding generative standard deviation (mean ± 1 std. dev.).
• Figure 5: Two-dimensional probability density of the dataset, estimated via a GPU-accelerated Kernel Density Estimation (KDE). The optimal KDE hyperparameters (kernel type and bandwidth) were determined via 3-fold cross-validation on a random subset of 5,000 friction law curves. The final density was then computed on a larger sample of 16,384 curves using these optimal parameters. The x-axis represents the normal force $P$, and the y-axis represents the corresponding friction force $F$. The color intensity, plotted on a logarithmic scale, indicates the probability density, defining the valid physical domain for our generative models.