Related papers: Schr\"odinger-Inspired Time-Evolution for 4D Defor…

Considering the inherent stochasticity and uncertainty, predicting future video frames is exceptionally challenging. In this work, we study the problem of video prediction by combining interpretability of stochastic state space models and…

Multi-dimensional direct numerical simulation (DNS) of the Schr\"odinger equation is needed for design and analysis of quantum nanostructures that offer numerous applications in biology, medicine, materials, electronic/photonic devices,…

The conventional, time-dependent Schroedinger equation describes only unidirectional time evolution of the state of a physical system, i.e., forward or, less commonly, backward. This paper proposes a generalized quantum dynamics for the…

The synthesis of spatiotemporally coherent 4D content presents fundamental challenges in computer vision, requiring simultaneous modeling of high-fidelity spatial representations and physically plausible temporal dynamics. Current…

Deep operator networks (DeepONets) are powerful architectures for fast and accurate emulation of complex dynamics. As their remarkable generalization capabilities are primarily enabled by their projection-based attribute, we investigate…

We establish dispersive estimates and local decay estimates for the time evolution of non-self-adjoint matrix Schr\"odinger operators with threshold resonances in one space dimension. In particular, we show that the decay rates in the…

Temporal volume images with 3D+t (4D) information are often used in medical imaging to statistically analyze temporal dynamics or capture disease progression. Although deep-learning-based generative models for natural images have been…

Intraoperative 2D/3D registration aligns preoperative 3D volumes with real-time 2D radiographs, enabling accurate localization of instruments and implants. A recent fully differentiable similarity learning framework approximates geodesic…

In the study of shapes of human organs using computational anatomy, variations are found to arise from inter-subject anatomical differences, disease-specific effects, and measurement noise. This paper introduces a stochastic model for…

3D geometric contents are becoming increasingly popular. In this paper, we study the problem of analyzing deforming 3D meshes using deep neural networks. Deforming 3D meshes are flexible to represent 3D animation sequences as well as…

Recent 4D shape representations model continuous temporal evolution of implicit shapes by (1) learning query flows without leveraging shape and articulation priors or (2) decoding shape occupancies separately for each time value. Thus, they…

The problem of Schr\"odinger propagation of a discontinuous wavefunction -diffraction in time- is studied under a new light. It is shown that the evolution map in phase space induces a set of affine transformations on discontinuous…

Neural Operators (NOs) have emerged as powerful tools for learning mappings between function spaces. Among them, the kernel integral operator has been widely used in universally approximating architectures. Following the original…

We present ShapeFlow, a flow-based model for learning a deformation space for entire classes of 3D shapes with large intra-class variations. ShapeFlow allows learning a multi-template deformation space that is agnostic to shape topology,…

We present an operator learning approach for a class of evolution operators using a composition of a learned lift into the space of diffeomorphisms of the domain and the group action on the field space. In turn, this transforms the…

In this paper, we propose a method for characterizing 3D shapes from point clouds and we show a direct application on a study of organ temporal deformations. As an example, we characterize the behavior of a bladder during a forced…

The modeling and prediction of the ultrafast nonlinear dynamics in the optical fiber are essential for the studies of laser design, experimental optimization, and other fundamental applications. The traditional propagation modeling method…

Video-conditioned 4D shape generation aims to recover time-varying 3D geometry and view-consistent appearance directly from an input video. In this work, we introduce a native video-to-4D shape generation framework that synthesizes a single…

Biological systems commonly exhibit complex spatiotemporal patterns whose underlying generative mechanisms pose a significant analytical challenge. Traditional approaches to spatiodynamic inference rely on dimensionality reduction through…

Diffusion models have recently emerged as powerful frameworks for generating high-quality images. While recent studies have explored their application to time series forecasting, these approaches face significant challenges in cross-modal…