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Diffusion models have achieved remarkable success as generative models. However, even a well-trained model can accumulate errors throughout the generation process. These errors become particularly problematic when arbitrary guidance is…
We derive a variational expression for the correlation time of physical observables in steady-state diffusive systems. As a consequence of this variational expression, we obtain lower bounds on the correlation time, which provide speed…
We address the reachability problem for continuous-time stochastic dynamic systems. Our objective is to present a unified framework that characterizes the reachable set of a dynamic system in the presence of both stochastic disturbances and…
Continuous time random Walk model has been versatile analytical formalism for studying and modeling diffusion processes in heterogeneous structures, such as disordered or porous media. We are studying the continuous limits of Heterogeneous…
We propose a framework for analyzing the sensitivity of counterfactuals to parametric assumptions about the distribution of latent variables in structural models. In particular, we derive bounds on counterfactuals as the distribution of…
Generative models often treat continuous data and discrete events as separate processes, creating a gap in modeling complex systems where they interact synchronously. To bridge this gap, we introduce JointDiff, a novel diffusion framework…
Excitation energy transfer in light-harvesting aggregates is highly efficient, yet whether quantum coherence plays an operational role in transport remains debated. A central challenge is that coherence is usually inferred from…
Generative models are designed to address the data scarcity problem. Even with the exploding amount of data, due to computational advancements, some applications (e.g., health care, weather forecast, fault detection) still suffer from data…
Imagine generating a city's electricity demand pattern based on weather, the presence of an electric vehicle, and location, which could be used for capacity planning during a winter freeze. Such real-world time series are often enriched…
This work explores the trade-off between the number of samples required to accurately build models of dynamical systems and the degradation of performance in various control objectives due to a coarse approximation. In particular, we show…
Inspired by classical sensitivity results for nonlinear optimization, we derive and discuss new quantitative bounds to characterize the solution map and dual variables of a parametrized nonlinear program. In particular, we derive explicit…
We derive global estimates for the error in solutions of linear hyperbolic systems due to inaccurate boundary geometry. We show that the error is bounded by data and bounded in time when the solutions in the true and approximate domains are…
Energy systems modeling frequently relies on time series data, whether observed or forecast. This is particularly the case, for example, in capacity planning models that use hourly production and load data forecast to occur over the coming…
We present an approach for satisfying state constraints in systems with nonparametric uncertainty by estimating this uncertainty with a real-time-update Gaussian process (GP) model. Notably, new data is incorporated into the model in real…
The spectacular success of deep generative models calls for quantitative tools to measure their statistical performance. Divergence frontiers have recently been proposed as an evaluation framework for generative models, due to their ability…
Developing robot controllers in a simulated environment is advantageous but transferring the controllers to the target environment presents challenges, often referred to as the "sim-to-real gap". We present a method for continuous…
Pipe flow models are developed with a focus on their eventual use for feedback control design at the process control level, as opposed to the unit level, in gas processing facilities. Accordingly, linearized facility-scale models are…
The sensitivity parameter is widely used for quantifying fine tuning. However, examples show it fails to give correct results under certain circumstances. We argue that these problems only occur when calculating the sensitivity of a…
The integration of more intermittent generation, energy storage, and dynamic loads on top of a competitive market environment requires future grids to handle increasing diversity of power injection states. Grid planners need new tools and…
There has been a recent surge of interest in time series modeling using the Transformer architecture. However, forecasting multivariate time series with Transformer presents a unique challenge as it requires modeling both temporal…