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Many systems may switch to an undesired state due to internal failures or external perturbations, of which critical transitions toward degraded ecosystem states are a prominent example. Resilience restoration focuses on the ability of…
This study examines the challenges of modeling complex and noisy data related to socioeconomic factors over time, with a focus on data from various districts in Odisha, India. Traditional time-series models struggle to capture both trends…
Understanding the principles that govern dynamical systems is a central challenge across many scientific domains, including biology and ecology. Incomplete knowledge of nonlinear interactions and stochastic effects often renders bottom-up…
It is critical yet challenging for deep learning models to properly characterize uncertainty that is pervasive in real-world environments. Although a lot of efforts have been made, such as heteroscedastic neural networks (HNNs), little work…
Stochastic learning dynamics based on Langevin or Levy stochastic differential equations (SDEs) in deep neural networks control the variance of noise by varying the size of the mini-batch or directly those of injecting noise. Since the…
Neural Ordinary Differential Equation (Neural ODE) has been proposed as a continuous approximation to the ResNet architecture. Some commonly used regularization mechanisms in discrete neural networks (e.g. dropout, Gaussian noise) are…
Regulation of intrinsic noise in gene expression is essential for many cellular functions. Correspondingly, there is considerable interest in understanding how different molecular mechanisms of gene expression impact variations in protein…
The intrinsic stochasticity of gene expression can lead to large variability of protein levels across a population of cells. Variability (or noise) in protein distributions can be modulated by cellular mechanisms of gene regulation; in…
A central challenge in computational modeling of dynamic biological systems is parameter inference from experimental time course measurements. However, one would not only like to infer kinetic parameters but also study their variability…
Reversible electropermeabilization, commonly referred to as electroporation, is a transient increase in cell membrane permeability induced by short, high-voltage electric pulses. We present a stochastically perturbed version of a…
This paper presents a stochastic differential equation (SDE) approach for general-purpose image restoration. The key construction consists in a mean-reverting SDE that transforms a high-quality image into a degraded counterpart as a mean…
We propose robust methods to identify underlying Partial Differential Equation (PDE) from a given set of noisy time dependent data. We assume that the governing equation is a linear combination of a few linear and nonlinear differential…
We study identifiability of stochastic differential equations (SDE) under multiple interventions. Our results give the first provable bounds for unique recovery of SDE parameters given samples from their stationary distributions. We give…
This study addresses the inverse problem of parameter estimation for Stochastic Differential Equations (SDEs) by minimizing a regularized discrepancy functional via Stochastic Gradient Descent (SGD). To achieve computational efficiency, we…
Measurement noise is an integral part while collecting data of a physical process. Thus, noise removal is necessary to draw conclusions from these data, and it often becomes essential to construct dynamical models using these data. We…
Gene expression is stochastic and displays variation ("noise") both within and between cells. Intracellular (intrinsic) variance can be distinguished from extracellular (extrinsic) variance by applying the law of total variance to data from…
Cross-domain speech enhancement (SE) is often faced with severe challenges due to the scarcity of noise and background information in an unseen target domain, leading to a mismatch between training and test conditions. This study puts…
Identifying unknown differential equations from a given set of discrete time dependent data is a challenging problem. A small amount of noise can make the recovery unstable, and nonlinearity and differential equations with varying…
Stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs) are fundamental for modeling stochastic dynamics across the natural sciences and modern machine learning. Learning their solution operators with…
The paradigm of stochastic resonance (SR)---the idea that signal detection and transmission may benefit from noise---has met with great interest in both physics and the neurosciences. We investigate here the consequences of reducing the…