Related papers: Automatic Differentiation for Orbital-Free Density…
We introduce a framework for automatic differentiation with weighted finite-state transducers (WFSTs) allowing them to be used dynamically at training time. Through the separation of graphs from operations on graphs, this framework enables…
We develop a new and general encode-approximate-reconstruct operator learning model that leverages learned neural representations of bases for input and output function distributions. We introduce the concepts of \textit{numerical operator…
Automatic differentiation is a key component in deep learning. This topic is well studied and excellent surveys such as Baydin et al. (2018) have been available to clearly describe the basic concepts. Further, sophisticated implementations…
We present differentiable particle filters (DPFs): a differentiable implementation of the particle filter algorithm with learnable motion and measurement models. Since DPFs are end-to-end differentiable, we can efficiently train their…
A characteristic feature of differential-algebraic equations is that one needs to find derivatives of some of their equations with respect to time, as part of so called index reduction or regularisation, to prepare them for numerical…
High-throughput computational screening has emerged as a critical component of materials discovery. Direct density functional theory (DFT) simulation of inorganic materials and molecular transition metal complexes is often used to describe…
We present the classical coordinate-free formalism for forward and backward mode ad in the real and complex setting. We show how to formally derive the forward and backward formulae for a number of matrix functions starting from basic…
Stochastic and mixed stochastic-deterministic density functional theory (DFT) are promising new approaches for the calculation of the equation-of-state and transport properties in materials under extreme conditions. In the intermediate warm…
Density Functional Theory (DFT) is one of the most widely used methods for "ab initio" calculations of the structure of atoms, molecules, crystals, surfaces, and their interactions. Unfortunately, the customary introduction to DFT is often…
The scientific computation methods development in conjunction with artificial intelligence technologies remains a hot research topic. Finding a balance between lightweight and accurate computations is a solid foundation for this direction.…
The use of derivative-based solvers to compute solutions to optimal control problems with non-differentiable cost or dynamics often requires reformulations or relaxations that complicate the implementation or increase computational…
Complex dynamic systems are typically either modeled using expert knowledge in the form of differential equations or via data-driven universal approximation models such as artificial neural networks (ANN). While the first approach has…
Particle filters are not compatible with automatic differentiation due to the presence of discrete resampling steps. While known estimators for the score function, based on Fisher's identity, can be computed using particle filters, up to…
The journey of theoretical study on semiconductors is reviewed in a non-conventional way. We have started with the basic introduction of Hartree-Fock method and introduce the fundamentals of Density Functional Theory (DFT). From the oldest…
The accuracy of atomistic simulations depends on the precision of force fields. Traditional numerical methods often struggle to optimize the empirical force field parameters for reproducing target properties. Recent approaches rely on…
We apply program verification technology to the problem of specifying and verifying automatic differentiation (AD) algorithms. We focus on define-by-run, a style of AD where the program that must be differentiated is executed and monitored…
We consider the problem of OOD generalization, where the goal is to train a model that performs well on test distributions that are different from the training distribution. Deep learning models are known to be fragile to such shifts and…
Predicting interfacial thermodynamics across molecular and continuum scales remains a central challenge in computational science. Classical density functional theory (cDFT) provides a first-principles route to connect microscopic…
Density Functional Theory (DFT) has become a cornerstone in the modeling of metals. However, accurately simulating metals, particularly under extreme conditions, presents two significant challenges. First, simulating complex metallic…
Automatic differentiation (AD) aims to compute derivatives of user-defined functions, but in Turing-complete languages, this simple specification does not fully capture AD's behavior: AD sometimes disagrees with the true derivative of a…