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Surrogate models have shown to be an extremely efficient aid in solving engineering problems that require repeated evaluations of an expensive computational model. They are built by sparsely evaluating the costly original model and have…
Monitoring ground displacement is crucial for urban infrastructure stability and mitigating geological hazards. However, forecasting future deformation from sparse Interferometric Synthetic Aperture Radar (InSAR) time-series data remains a…
Many imaging problems require computing spatial transformations induced by spatially varying intensity, feature, or density fields. Canonical examples include distortion correction, deformable image registration, atlas-based segmentation,…
Standard methods in computer model calibration treat the calibration parameters as constant throughout the domain of control inputs. In many applications, systematic variation may cause the best values for the calibration parameters to…
Multivariate spatially-oriented data sets are prevalent in the environmental and physical sciences. Scientists seek to jointly model multiple variables, each indexed by a spatial location, to capture any underlying spatial association for…
We explore the idea that non-equilibrium steady states breaking detailed balance are obtained by deforming trajectories (lines in space-time) that have been sampled in a reference system with stochastic dynamics obeying detailed balance,…
The recent experimental progresses in handling microscopic systems have allowed to probe them at levels where fluctuations are prominent, calling for stochastic modeling in a large number of physical, chemical and biological phenomena. This…
We introduce a method for decomposition of trend, cycle and seasonal components in spatio-temporal models and apply it to investigate the existence of climate changes in temperature and rainfall series. The method incorporates critical…
The modeling of coupled fluid transport and deformation in a porous medium is essential to predict the various geomechanical process such as CO2 sequestration, hydraulic fracturing, and so on. Current applications of interest, for instance,…
Due to spatial dependence -- often characterized as complex and non-linear -- model misspecification is a prevalent and critical issue in spatial data analysis and prediction. As the data, and thus model performance, is heterogeneous,…
There is a growing interest in developing covariance functions for processes on the surface of a sphere due to wide availability of data on the globe. Utilizing the one-to-one mapping between the Euclidean distance and the great circle…
This paper studies a regression model with functional dependent and explanatory variables, both of which exhibit nonstationary dynamics. The model assumes that the nonstationary stochastic trends of the dependent variable are explained by…
Modeling arbitrarily large deformations of surfaces smoothly embedded in three-dimensional space is challenging. The difficulties come from two aspects: the existing geometry processing or forward simulation methods penalize the difference…
The original Hardenberg's model of biomass patterns in arid and semi-arid regions is revisited to extend it to more general non flat regions. It is proposed a technique to study these more generalized (non-flat) regions using both a…
We introduce a generalized machine learning framework to probabilistically parameterize upper-scale models in the form of nonlinear PDEs consistent with a continuum theory, based on coarse-grained atomistic simulation data of mechanical…
A stochastic deformation of a thermodynamic symplectic structure is studied. The stochastic deformation procedure is analogous to the deformation of an algebra of observables like deformation quantization, but for an imaginary deformation…
Spatio-temporal processes in environmental applications are often assumed to follow a Gaussian model, possibly after some transformation. However, heterogeneity in space and time might have a pattern that will not be accommodated by…
Recent developments in engineering techniques for spatial data collection such as geographic information systems have resulted in an increasing need for methods to analyze large spatial data sets. These sorts of data sets can be found in…
In spatial regression models, spatial heterogeneity may be considered with either continuous or discrete specifications. The latter is related to delineation of spatially connected regions with homogeneous relationships between variables…
A class of random non-stationary signals termed timbre x dynamics is introduced and studied. These signals are obtained by non-linear transformations of sta-tionary random gaussian signals, in such a way that the transformation can be…