Atomic-scale simulations provide a computational method to probe the properties of
molecules and materials. Their predictive power is highest when the interactions
between atoms are obtained from electronic-structure theory, but the cost of
these calculations limits the accessible system sizes, time scales, and
statistical accuracy. Machine learning offers a way to overcome these limitations:
expensive quantum-mechanical calculations can be replaced by much faster regression
models trained on reference data. The central difficulty is not only to make
these models accurate, but to make them useful in scientific simulations.
This thesis develops machine-learning methods for atomic-scale modeling along
two connected directions. The first is the construction of physically faithful
representations and architectures for predicting structure-property maps. Particular
emphasis is placed on the role of physical priors such as locality, smoothness,
symmetry, and body-order character, and how they can be incorporated into descriptors,
kernels, and neural networks. This includes smooth bases for atom-centered
representations, body-ordered equivariant kernels, and architectures that use physical
preconditioning without imposing restrictive truncations. The opposite limit is
also examined, in which some symmetries or conservation laws are relaxed,
showing when this leads to improved accuracy and efficiency, and when
it instead results in qualitative failures of simulations. The resulting unconstrained
models are especially valuable for developing universal interatomic potentials that
aim to cover large regions of chemical and configurational space.
These models make it possible to perform advanced simulations out of the box,
but they also expose the need for careful validation and uncertainty quantification. To
address this issue, the thesis introduces prediction-rigidity methods that
provide low-cost uncertainty estimates for trained neural networks and can be
propagated to downstream properties and simulation workflows.
The second direction is molecular dynamics beyond conventional time integration.
Machine-learned potentials accelerate force evaluation, but they still inherit
the very small time steps required by the numerical integration of atomistic
motion. This thesis investigates models that predict long strides of molecular
dynamics directly,
thereby replacing many numerical integration steps by a single learned map.
These direct predictors can reproduce equilibrium and time-dependent properties
over much longer effective time scales, but they also introduce failure modes
that are specific to trajectory prediction. The geometric structure of
Hamiltonian mechanics can be restored by learning symplectic and time-reversible
maps, which is equivalent to learning the classical action that generates the dynamics.
Together, these results outline a pragmatic view of atomistic machine learning.
Accuracy on benchmark data is only one part of the problem. Usef
