Related papers: Path-Integral Formulation of Unavoidable Canonical…
When we consider canonical averages for classical discrete systems, typically referred to as substitutional alloys, the map phi from many-body interatomic interactions to thermodynamic equilibrium configurations generally exhibits…
For classical discrete systems under constant composition, canonical average provides equilibrium configuration from a set of many-body interactions, which typically acts as nonlinear map. The nonlinearity has recently been investigated in…
When we consider discretization of continuous probability distributions, it inevitably induces irreversible geometric distortion of local measure on the discretized support. While such discretziation-induced distortion is extrinsic to…
For classical discrete systems under constant composition (typically reffered to as substitutional alloys), canonical average can act as a map from a set of many-body interatomic interactions to that of configuration in thermodynamic…
Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving PDEs, yet existing uncertainty quantification (UQ) approaches for PINNs generally lack rigorous statistical guarantees. In this work, we bridge this…
This paper introduces Uncertainty Propagation Network (UPN), a novel family of neural differential equations that naturally incorporate uncertainty quantification into continuous-time modeling. Unlike existing neural ODEs that predict only…
When we consider canonical average for classical discrete systems under constant composition (specifically, substitutional alloys) as a map phi from a set of many-body interatomic interactions to that of microscopic configuration in…
Quantification of uncertainty in production/injection forecasting is an important aspect of reservoir simulation studies. Conventional approaches include intrusive Galerkin-based methods (e.g., generalized polynomial chaos (gPC) and…
This paper analyzes a full discretization of a three-dimensional stochastic Allen-Cahn equation with multiplicative noise. The discretization combines the Euler scheme for temporal approximation and the finite element method for spatial…
Since the invention of generalized polynomial chaos in 2002, uncertainty quantification has impacted many engineering fields, including variation-aware design automation of integrated circuits and integrated photonics. Due to the fast…
We develop a systematic information-theoretic framework for quantification and mitigation of error in probabilistic Lagrangian (i.e., path-based) predictions which are obtained from dynamical systems generated by uncertain (Eulerian) vector…
Simulating complex physical systems is crucial for understanding and predicting phenomena across diverse fields, such as fluid dynamics and heat transfer, as well as plasma physics and structural mechanics. Traditional approaches rely on…
In this article, we study unbalanced optimal transport (UOT) and establish a control-theoretic dynamical extension, which we call the unbalanced density control (UDC), for a class of Gaussian reference measures. In the static setting, we…
For classical discrete system under constant composition, typically reffered to as substitutional alloys, correspondence between interatomic many-body interactions and structure in thermodynamic equilibrium exhibit profound, complicated…
Graph Convolutional Networks (GCNs) have shown to be effective in handling unordered data like point clouds and meshes. In this work we propose novel approaches for graph convolution, pooling and unpooling, inspired from finite differences…
Unbalanced optimal transport (UOT) provides a flexible way to match or compare nonnegative finite Radon measures. However, UOT requires a predefined ground transport cost, which may misrepresent the data's underlying geometry. Choosing such…
We consider proposals for the cost of holographic path integrals. Gravitational path integrals within finite radial cutoff surfaces have a precise map to path integrals in $T\bar T$ deformed holographic CFTs. In Nielsen's geometric…
Despite the great promise of the physics-informed neural networks (PINNs) in solving forward and inverse problems, several technical challenges are present as roadblocks for more complex and realistic applications. First, most existing…
Modeling statistical regularity plays an essential role in ill-posed image processing problems. Recently, deep learning based methods have been presented to implicitly learn statistical representation of pixel distributions in natural…
In this work, we study the influence of domain-specific characteristics when defining a meaningful notion of predictive uncertainty on graph data. Previously, the so-called Graph Posterior Network (GPN) model has been proposed to quantify…