相关论文: Mathematical foundation of Information Field Dynam…

Modern deep learning architectures excel at optimization, but only after the data has entered the network. The true bottleneck lies in preparing the right input: minimal, salient, and structured in a way that reflects the essential patterns…

Numerous biological and physical processes can be modeled as systems of interacting entities evolving continuously over time, e.g. the dynamics of communicating cells or physical particles. Learning the dynamics of such systems is essential…

We consider the problems of clustering, classification, and visualization of high-dimensional data when no straightforward Euclidean representation exists. Typically, these tasks are performed by first reducing the high-dimensional data to…

Deep learning (DL) is a powerful tool in computational imaging for many applications. A common strategy is to reconstruct a preliminary image as the input of a neural network to achieve an optimized image. Usually, the preliminary image is…

With the increased penetrations of distributed energy resources (DERs), the need for integrated transmission and distribution system analysis (T&D) is imperative. This paper presents an integrated unbalanced T&D analysis framework using an…

Solving Partial Differential Equations (PDEs) is the core of many fields of science and engineering. While classical approaches are often prohibitively slow, machine learning models often fail to incorporate complete system information.…

The thoracic diaphragm is the muscle that drives the respiratory cycle of a human being. Using a system of partial differential equations (PDEs) that models linear elasticity we compute displacements and stresses in a two-dimensional cross…

We present a novel, fast differentiable simulator for soft-body learning and control applications. Existing differentiable soft-body simulators can be classified into two categories based on their time integration methods: Simulators using…

Cognitive computation such as e.g. language processing, is conventionally regarded as Turing computation, and Turing machines can be uniquely implemented as nonlinear dynamical systems using generalized shifts and subsequent G\"odel…

The growth of computational resources in the past decades has expanded the application of Computational Fluid Dynamics (CFD) from the traditional fields of aerodynamics and hydrodynamics to a number of new areas. Examples range from the…

Progress towards the energy breakthroughs needed to combat climate change can be significantly accelerated through the efficient simulation of atomic systems. Simulation techniques based on first principles, such as Density Functional…

The Stefan problem is a classical free-boundary problem that models phase-change processes and poses computational challenges due to its moving interface and nonlinear temperature-phase coupling. In this work, we develop a physics-informed…

Quantum many-body dynamics generically results in increasing entanglement that eventually leads to thermalization of local observables. This makes the exact description of the dynamics complex despite the apparent simplicity of…

Conventional molecular dynamics (MD) simulation approaches, such as $\textit{ab initio}$ MD (AIMD) and empirical force field MD (EFFMD), face significant trade-offs between physical accuracy and computational efficiency. This work presents…

Random fields are useful mathematical objects in the characterization of non-deterministic complex systems. A fundamental issue in the evolution of dynamical systems is how intrinsic properties of such structures change in time. In this…

The Fisher information matrix (FIM) is fundamental to understanding the trainability of deep neural nets (DNN), since it describes the parameter space's local metric. We investigate the spectral distribution of the conditional FIM, which is…

Recent work has made significant progress on using implicit functions, as a continuous representation for 3D rigid object shape reconstruction. However, much less effort has been devoted to modeling general articulated objects. Compared to…

We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled…

The Fisher information matrix (FIM) is a foundational concept in statistical signal processing. The FIM depends on the probability distribution, assumed to belong to a smooth parametric family. Traditional approaches to estimating the FIM…

This paper establishes a mathematical foundation for the Adam optimizer, elucidating its connection to natural gradient descent through Riemannian and information geometry. We provide an accessible and detailed analysis of the diagonal…