Related papers: Property-driven State-Space Coarsening for Continu…
Modeling data with non-stationary covariance structure is important to represent heterogeneity in geophysical and other environmental spatial processes. In this work, we investigate a multistage approach to modeling non-stationary…
Lumping a Markov process introduces a coarser level of description that is useful in many contexts and applications. The dynamics on the coarse grained states is often approximated by its Markovian component. In this letter we derive…
High-dimensional recordings of dynamical processes are often characterized by a much smaller set of effective variables, evolving on low-dimensional manifolds. Identifying these latent dynamics requires solving two intertwined problems:…
Coarse-graining (CG) of molecular simulations simplifies the particle representation by grouping selected atoms into pseudo-beads and drastically accelerates simulation. However, such CG procedure induces information losses, which makes…
We develop a quadratic regularization approach for the solution of high-dimensional multistage stochastic optimization problems characterized by a potentially large number of time periods/stages (e.g. hundreds), a high-dimensional resource…
Matrix factorization from a small number of observed entries has recently garnered much attention as the key ingredient of successful recommendation systems. One unresolved problem in this area is how to adapt current methods to handle…
Spatial multiscale methods have established themselves as useful tools for extending the length scales accessible by conventional statics (i.e., zero temperature molecular dynamics). Recently, extensions of these methods, such as the…
The vast combination of material properties seen in nature are achieved by the complexity of the material microstructure. Advanced characterization and physics based simulation techniques have led to generation of extremely large…
A generalized understanding of protein dynamics is an unsolved scientific problem, the solution of which is critical to the interpretation of the structure-function relationships that govern essential biological processes. Here, we approach…
Given (small amounts of) time-series' data from a high-dimensional, fine-grained, multiscale dynamical system, we propose a generative framework for learning an effective, lower-dimensional, coarse-grained dynamical model that is predictive…
We implemented a coarse-graining procedure to construct mesoscopic models of complex molecules. The final aim is to obtain better results on properties depending on slow modes of the molecules. Therefore the number of particles considered…
Due to the high computational load of modern numerical simulation, there is a demand for approaches that would reduce the size of discrete problems while keeping the accuracy reasonable. In this work, we present an original algorithm to…
Coarse-grained (CG) models provide an effective route to reducing the complexity of molecular simulations (MD), but conventional approaches depend heavily on long all-atom MD trajectories to adequately sample configurational space. This…
This paper details how to parameterize the posterior distribution of state-space systems to generate improved optimization problems for system identification using variational inference. Three different parameterizations of the assumed…
The modeling of complicated time-evolving physical dynamics from partial observations is a long-standing challenge. Particularly, observations can be sparsely distributed in a seemingly random or unstructured manner, making it difficult to…
Brute-force simulations for dynamics on very large networks are quite expensive. While phenomenological treatments may capture some macroscopic properties, they often ignore important microscopic details. Fortunately, one may be only…
Coupled natural systems are generally modeled at multiple abstraction levels. Both structural scale and behavioral complexity of these models are determinants in the kinds of questions that can be posed and answered. As scale and complexity…
Accurately predicting the long-term behavior of chaotic systems is crucial for various applications such as climate modeling. However, achieving such predictions typically requires iterative computations over a dense spatiotemporal grid to…
Dynamic scene rendering has taken a leap forward with the rise of 4D Gaussian Splatting, but there's still one elusive challenge: how to make 3D Gaussians move through time as naturally as they would in the real world, all while keeping the…
A brief review of modeling and simulation methods for a study of polymers at interfaces is provided. When studying truly multiscale problems as provided by realistic polymer systems, coarse graining is practically unavoidable. In this…