Related papers: Data-driven reconstruction of spatiotemporal phase…
A variational approach to reconstruction of phase and amplitude of a complex-valued object from Poissonian intensity observations is developed. The observation model corresponds to the typical optical setups with a phase modulation of…
Thermodynamic conventions suffer from describing dynamical distinctions, especially when the structural and energetic changes induced by localized rare events are insignificant. By using the ensemble theory in the trajectory space, we…
High-fidelity simulation of complex physical systems is exorbitantly expensive and inaccessible across spatiotemporal scales. Recently, there has been an increasing interest in leveraging deep learning to augment scientific data based on…
The sea surface temperature (SST), a key environmental parameter, is crucial to optimizing production planning, making its accurate prediction a vital research topic. However, the inherent nonlinearity of the marine dynamic system presents…
Atmospheric trace-gas inversion refers to any technique used to predict spatial and temporal fluxes using mole-fraction measurements and atmospheric simulations obtained from computer models. Studies to date are most often of a…
Natural systems are typically nonlinear and complex, and it is of great interest to be able to reconstruct a system in order to understand its mechanism, which can not only recover nonlinear behaviors but also predict future dynamics. Due…
The location, timing, and abundance of gene expression (both mRNA and proteins) within a tissue define the molecular mechanisms of cell functions. Recent technology breakthroughs in spatial molecular profiling, including imaging-based…
In this paper we present a general framework in which one can rigorously study the effect of spatio-temporal noise on traveling waves, stationary patterns and oscillations that are invariant under the action of a finite-dimensional set of…
We study data-driven stabilization of continuous-time systems in autoregressive form when only noisy input-output data are available. First, we provide an operator-based characterization of the set of systems consistent with the data. Next,…
Spatio-temporal forecasting has numerous applications in analyzing wireless, traffic, and financial networks. Many classical statistical models often fall short in handling the complexity and high non-linearity present in time-series data.…
Positron emission tomography (PET) is a classical imaging technique to reconstruct the mass distribution of a radioactive material. If the mass distribution is static, this essentially leads to inversion of the X-ray transform. However, if…
A variational inference-based framework for training a multi-output Gaussian process latent variable model, specifically tailored to the tails-up spatio-temporal stream network, is developed. Training, given a censored observational data…
We present a numerical framework for recovering unknown non-autonomous dynamical systems with time-dependent inputs. To circumvent the difficulty presented by the non-autonomous nature of the system, our method transforms the solution state…
We consider the problem of estimating the transition dynamics $T^*$ from near-optimal expert trajectories in the context of offline model-based reinforcement learning. We develop a novel constraint-based method, Inverse Transition Learning,…
Mathematical models of spatial population dynamics typically focus on the interplay between dispersal events and birth/death processes. However, for many animal communities, significant arrangement in space can occur on shorter timescales,…
In this paper, we consider the travel time tomography problem for conformal metrics on a bounded domain, which seeks to determine the conformal factor of the metric from the lengths of geodesics joining boundary points. We establish forward…
We propose a novel approach for modelling bat motion dynamics and use it to predict roost locations using data from static acoustic detectors. Specifically, radio tracking studies of Greater Horseshoe bats demonstrate that bat movement can…
We introduce a Bayesian model for estimating the distribution of ambulance travel times on each road segment in a city, using Global Positioning System (GPS) data. Due to sparseness and error in the GPS data, the exact ambulance paths and…
Providing transport users and operators with accurate forecasts on travel times is challenging due to a highly stochastic traffic environment. Public transport users are particularly sensitive to unexpected waiting times, which negatively…
We show that the probability distribution function that best fits the distribution of return times between two consecutive visits of a chaotic trajectory to finite size regions in phase space deviates from the exponential statistics by a…