Related papers: Automatic Differentiation for Orbital-Free Density…

Automatic differentiation (AD) is a set of techniques that systematically applies the chain rule to compute the gradients of functions without requiring human intervention. Although the fundamentals of this technology were established…

Uncovering the underlying ordinary differential equations (ODEs) that govern dynamic systems is crucial for advancing our understanding of complex phenomena. Traditional symbolic regression methods often struggle to capture the temporal…

The Mat\'ern covariance function is ubiquitous in the application of Gaussian processes to spatial statistics and beyond. Perhaps the most important reason for this is that the smoothness parameter $\nu$ gives complete control over the…

A real-space formalism for density-functional perturbation theory (DFPT) is derived and applied for the computation of harmonic vibrational properties in molecules and solids. The practical implementation using numeric atom-centered…

Differentiable Filters, as recursive Bayesian estimators, possess the ability to learn complex dynamics by deriving state transition and measurement models exclusively from data. This data-driven approach eliminates the reliance on explicit…

We study the correctness of automatic differentiation (AD) in the context of a higher-order, Turing-complete language (PCF with real numbers), both in forward and reverse mode. Our main result is that, under mild hypotheses on the primitive…

Rapid advances in deep learning have brought not only myriad powerful neural networks, but also breakthroughs that benefit established scientific research. In particular, automatic differentiation (AD) tools and computational accelerators…

Density functional theory (DFT) embedding provides a formally exact framework for interfacing correlated wave-function theory (WFT) methods with lower-level descriptions of electronic structure. Here, we report techniques to improve the…

Continual learning, enabling models to acquire new skills and knowledge without degrading existing capabilities, remains a fundamental challenge for foundation models. While on-policy reinforcement learning can reduce forgetting, it…

Automatic differentiation is a tool for numerically calculating derivatives of a given function up to machine precision. This tool is useful for quantum chemistry methods, which require the calculation of gradients either for the…

Orbital-free density functional theory promises to deliver linear-scaling electronic structure calculations. This requires the knowledge of the non-interacting kinetic-energy density functional (KEDF), which should be accurate and must…

The auto differentiable simulation is a type of simulation that outputs of the simulation include not only the simulation result itself, but also their derivatives with respect to various input parameters. It provides an efficient method to…

Probabilistic modeling is iterative. A scientist posits a simple model, fits it to her data, refines it according to her analysis, and repeats. However, fitting complex models to large data is a bottleneck in this process. Deriving…

Differentiation lies at the core of many machine-learning algorithms, and is well-supported by popular autodiff systems, such as TensorFlow and PyTorch. Originally, these systems have been developed to compute derivatives of differentiable…

Understanding fine-grained object affordances is imperative for robots to manipulate objects in unstructured environments given open-ended task instructions. However, existing methods of visual affordance predictions often rely on manually…

Density estimation plays a crucial role in many data analysis tasks, as it infers a continuous probability density function (PDF) from discrete samples. Thus, it is used in tasks as diverse as analyzing population data, spatial locations in…

Linear discriminant analysis improves class separability but struggles with non-linearly separable data. To overcome this, we introduce Deep Discriminant Analysis (DDA), which directly optimizes the Fisher criterion utilizing deep networks.…

Accurate and efficient simulation tools are essential in robotics, enabling the visualization of system dynamics and the validation of control laws before committing resources to physical experimentation. Developing physically accurate…

Differential machine learning combines automatic adjoint differentiation (AAD) with modern machine learning (ML) in the context of risk management of financial Derivatives. We introduce novel algorithms for training fast, accurate pricing…

Simulations in the warm dense matter regime using finite temperature Kohn-Sham density functional theory (FT-KS-DFT), while frequently used, are computationally expensive due to the partial occupation of a very large number of high-energy…