Related papers: Noisy, sparse, nonlinear: Navigating the Bermuda T…

In this paper, we propose an optimization-based sparse learning approach to identify the set of most influential reactions in a chemical reaction network. This reduced set of reactions is then employed to construct a reduced chemical…

Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…

Discovering dynamical models to describe underlying dynamical behavior is essential to draw decisive conclusions and engineering studies, e.g., optimizing a process. Experimental data availability notwithstanding has increased…

We show how fitting sparse linear models over learned deep feature representations can lead to more debuggable neural networks. These networks remain highly accurate while also being more amenable to human interpretation, as we demonstrate…

A wide variety of real life complex networks are prohibitively large for modeling, analysis and control. Understanding the structure and dynamics of such networks entails creating a smaller representative network that preserves its relevant…

Chemical kinetic mechanisms can be represented by sets of elementary reactions that are easily translated into mathematical terms using physicochemical relationships. The schematic representation of reactions captures the interactions…

Data-driven discovery of governing equations from data remains a fundamental challenge in nonlinear dynamics. Although sparse regression techniques have advanced system identification, they struggle with rational functions and noise…

Sparse system identification of nonlinear dynamic systems is still challenging, especially for stiff and high-order differential equations for noisy measurement data. The use of highly correlated functions makes distinguishing between true…

We study parameter estimation in Nonlinear Factor Analysis (NFA) where the generative model is parameterized by a deep neural network. Recent work has focused on learning such models using inference (or recognition) networks; we identify a…

Identification of the particle interaction potential is a challenging and important task in dusty plasma, colloids, and smart materials as it allows the characterization of structure formation and helps predict phase transitions. With the…

We propose a technique to detect and generate patterns in a network of locally interacting dynamical systems. Central to our approach is a novel spatial superposition logic, whose semantics is defined over the quad-tree of a partitioned…

Obtaining system parameters and reconstructing the full flow state from limited velocity observations using conventional fluid dynamics solvers can be prohibitively expensive. Here we employ machine learning algorithms to overcome the…

The ability to discover physical laws and governing equations from data is one of humankind's greatest intellectual achievements. A quantitative understanding of dynamic constraints and balances in nature has facilitated rapid development…

In many problems of data-driven modeling for dynamical systems, the governing equations are not known a priori and must be selected phenomenologically from a large set of candidate interactions and basis functions. In such situations, point…

Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…

As machine learning continues to gain momentum in the neuroscience community, we witness the emergence of novel applications such as diagnostics, characterization, and treatment outcome prediction for psychiatric and neurological disorders,…

In this paper we present a theoretical analysis to understand sparse filtering, a recent and effective algorithm for unsupervised learning. The aim of this research is not to show whether or how well sparse filtering works, but to…

Deepfake detection models have achieved high accuracy in identifying synthetic media, but their decision processes remain largely opaque. In this paper we present a mechanistic interpretability framework for deepfake detection applied to a…

To improve the physical understanding and the predictions of complex dynamic systems, such as ocean dynamics and weather predictions, it is of paramount interest to identify interpretable models from coarsely and off-grid sampled…

Network models are widely used as structural summaries of biochemical systems. Statistical estimation of networks is usually based on linear or discrete models. However, the dynamics of these systems are generally nonlinear, suggesting that…