This accuracy makes it possible to derive properties such as energies and forces directly from the wavefunction in an end-to-end manner.

Bayesian optimization has become widely popular across various experimental sciences due to its favorable attributes: it can handle noisy data, perform well with relatively small datasets, and provide adaptive suggestions for sequential experimentation. While still in its infancy, Bayesian optimization has recently gained traction in bioprocess engineering. However, experimentation with biological systems is highly complex and the resulting experimental uncertainty requires specific extensions to classical Bayesian optimization. Moreover, current literature often targets readers with a strong statistical background, limiting its accessibility for practitioners. In light of these developments, this review has two aims: first, to provide an intuitive and practical introduction to Bayesian optimization; and second, to outline promising application areas and open algorithmic challenges, thereby highlighting opportunities for future research in machine learning.

Universal machine-learned potentials promise transferable accuracy across compositional and vibrational degrees of freedom, yet their application to biomolecular simulations remains underexplored. This work systematically evaluates equivariant message-passing architectures trained on the SPICE-v2 dataset with and without explicit long-range dispersion and electrostatics. We assess the impact of model size, training data composition, and electrostatic treatment across in- and out-of-distribution benchmark datasets, as well as molecular simulations of bulk liquid water, aqueous NaCl solutions, and biomolecules, including alanine tripeptide, the mini-protein Trp-cage, and Crambin. While larger models improve accuracy on benchmark datasets, this trend does not consistently extend to properties obtained from simulations. Predicted properties also depend on the composition of the training dataset. Long-range electrostatics show no systematic impact across systems. However, for Trp-cage, their inclusion yields increased conformational variability. Our results suggest that imbalanced datasets and immature evaluation practices currently challenge the applicability of universal machine-learned potentials to biomolecular simulations.

Table 4: Shared hyperparameters for all models, given for each task. Hyperparameter Random Walk Algorithm Reddit/BASE Enwik8 Layers 4 4 8 8 Hidden size 256 256 512 512 Head count 4 4 8 8 Dropout rate 0.2 0.2 0.3 0.3 Embed. We provide the hyperparameter setups shared across our models for each task in Table 4. Random Walk We train 4-layer models with a hidden size of 256 and 4 attention heads. Algorithm We train the 4-layer model with a hidden size of 256 and 4 attention heads. Staircase model which was run 5 times.

We prove the universal approximation theorem by showing the equivalence of TFN and our model. Complex spherical harmonics are related to Clebsch-Gordan coefficients via [51, 3.7.72] We can therefore adapt Eq. (2) by substituting C To see this, we look at the result's real component null [ H To prove this theorem we first introduce a proposition by Villar et al. [57]. GemNet's variance varies strongly between layers and increases significantly after each block without scaling factors (top). We use 4 stacked interaction blocks and an embedding size of 128 throughout the model.