Nonlinear dimensionality reduction and Bayesian optimization for accelerating design of materials

Optimizing biobased foam formulations is challenging because experiments are costly and fast-to-measure surrogate properties occupy high-dimensional spaces. Bayesian optimization (BO) with Gaussian process regression (GPR) can guide data-efficient searches, but its performance depends on the dimensionality of the inputs. Here, we evaluate nonlinear dimensionality reduction (DR) methods, namely t-distributed stochastic neighbor embedding (t-SNE) and uniform manifold approximation and projection (UMAP), in comparison with principal component analysis (PCA) for biobased foam optimization. Using an existing dataset comprising 26 distinct methylcellulose-cellulose fiber foam formulations with rheological and mechanical measurements, we first train a Gaussian process (GP) on low-dimensional representations of rheological observables. BO is then applied in a single-step, non-sequential manner on this fixed dataset, to evaluate the quality of the latent representations and identify high-yield-stress regions. A second GP maps foam-formulation compositions to the reduced rheological coordinates, enabling reconstruction of candidate formulations in the composition space. Across all DR methods, BO identifies similar high-performing formulations achieving yield stress values comparable to the experimentally validated optimum. PCA acts as a baseline due to its deterministic and hyperparameter-free nature, while nonlinear methods can achieve comparable performance when appropriately tuned. These findings demonstrate that nonlinear DR-assisted BO provides a data-efficient framework for optimizing rheology-governed soft-matter materials.