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We present a new piecewise linear regression methodology that utilizes fitting a difference of convex functions (DC functions) to the data. These are functions $f$ that may be represented as the difference $\phi_1 - \phi_2$ for a choice of…
Dissipated energy, representing a monotonically increasing state variable in nonlinear fracture mechanics, can be used as a restraint for tracing the dissipation instead of the elastic unloading path of the structure response. In this work,…
Resolvent analysis identifies the most responsive forcings and most receptive states of a dynamical system, in an input--output sense, based on its governing equations. Interest in the method has continued to grow during the past decade due…
In a landscape where scientific discovery is increasingly driven by data, the integration of machine learning (ML) with traditional scientific methodologies has emerged as a transformative approach. This paper introduces a novel,…
Probabilistic power flow (PPF) is essential for quantifying operational uncertainty in modern distribution systems with high penetration of renewable generation and flexible loads. Conventional PPF methods primarily rely on Monte Carlo (MC)…
We posit that autoregressive flow models are well-suited to performing a range of causal inference tasks - ranging from causal discovery to making interventional and counterfactual predictions. In particular, we exploit the fact that…
Increasingly demanding performance requirements for dynamical systems motivates the adoption of nonlinear and adaptive control techniques. One challenge is the nonlinearity of the resulting closed-loop system complicates verification that…
Non-parametric methods avoid the problem of having to specify a particular data generating mechanism, but can be computationally intensive, reducing their accessibility for large data problems. Empirical likelihood, a non-parametric…
Dynamic response evaluation in structural engineering is the process of determining the response of a structure, such as member forces, node displacements, etc when subjected to dynamic loads such as earthquakes, wind, or impact. This is an…
Real-time monitoring in modern medical research introduces functional longitudinal data, characterized by continuous-time measurements of outcomes, treatments, and confounders. This complexity leads to uncountably infinite…
Learning is a physical process. Here, we aim to study a simple dynamical system composed of springs and sticks capable of arbitrarily approximating any continuous function. The main idea of our work is to use the sticks to mimic a…
Physically-inspired latent force models offer an interpretable alternative to purely data driven tools for inference in dynamical systems. They carry the structure of differential equations and the flexibility of Gaussian processes,…
Short-term forecasting models typically assume the availability of input data (features) when they are deployed and in use. However, equipment failures, disruptions, cyberattacks, may lead to missing features when such models are used…
Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…
This paper investigates both biomechanical-constrained non-rigid medical image registrations and accurate identifications of material properties for soft tissues, using physics-informed neural networks (PINNs). The complex nonlinear…
Data-Driven Computational Mechanics is a novel computing paradigm that enables the transition from standard data-starved approaches to modern data-rich approaches. At this early stage of development, one can distinguish two mainstream…
Data from fluid flow measurements are typically sparse, noisy, and heterogeneous, often from mixed pressure and velocity measurements, resulting in incomplete datasets. In this paper, we develop a physics-constrained convolutional neural…
Reconstructing noise-driven nonlinear networks from time series of output variables is a challenging problem, which turns to be very difficult when nonlinearity of dynamics, strong noise impacts and low measurement frequencies jointly…
We revisit the problem of physics-informed regression, and propose a method that directly computes the state at the prediction point, simultaneously with the derivative and curvature information of the existing samples. We frame each…
In computational engineering, ensuring the integrity and safety of structures in fields such as aerospace and civil engineering relies on accurate stress prediction. However, analytical methods are limited to simple test cases, and…