Workshop II: Reduced Order Models

Machine-learned surrogates are reshaping atomistic simulation. The main examples are machine-learned interatomic potentials (MLIPs), machine-learned tight-binding (MLTB) and other reduced electronic-structure models, and coarse-grained molecular dynamics (CGMD). One of the most active areas of current research is the systematic treatment of long-range and non-bonded interactions such as electrostatics, polarization, and dispersion, which purely local models cannot capture. The workshop will bring together applied mathematicians, physicists, chemists, and ML researchers to examine the design of such models. Topics include how architectures such as equivariant networks and transformers encode physical structure, and when constraints such as symmetry, locality, and smoothness should be built in, imposed as priors, or learned from data. For coarse-grained models, challenges include how to identify collective variables. On the computational side, the workshop covers numerical methods and algorithms, including a reassessment of when low-precision arithmetic is acceptable in training and simulation. It also covers the software and data ecosystem that determines how efficiently methodological advances reach practitioners. A second theme is the learning theory of these models. Current theory largely targets generic architectures and transformers, and leaves open questions about the structured, physics-informed models typical of the field. These questions include training dynamics, implicit regularization and benign overfitting, and parameter identifiability and estimation. A key question is whether the inverse problem of constructing a reduced model from reference data is well-posed: if so, in what sense, and under what assumptions on the data? The aim is to connect these questions to architecture design and training protocols.