Related papers: Discovering PDEs from Multiple Experiments
Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…
One of the possible objectives when designing experiments is to build or formulate a model for predicting future observations. When the primary objective is prediction, some typical approaches in the planning phase are to use…
Parabolic partial differential equations (PDEs) appear in many disciplines to model the evolution of various mathematical objects, such as probability flows, value functions in control theory, and derivative prices in finance. It is often…
Many natural systems exhibit chaotic behaviour such as the weather, hydrology, neuroscience and population dynamics. Although many chaotic systems can be described by relatively simple dynamical equations, characterizing these systems can…
Regularizing continual learning techniques is important for anticipating algorithmic behavior under new realizations of data. We introduce a new approach to continual learning by imposing the properties of a parabolic partial differential…
Learning probabilistic models that can estimate the density of a given set of samples, and generate samples from that density, is one of the fundamental challenges in unsupervised machine learning. We introduce a new generative model based…
This study investigates the estimation and the statistical inference about Conditional Average Treatment Effects (CATEs), which have garnered attention as a metric representing individualized causal effects. In our data-generating process,…
The data-driven discovery of interpretable models approximating the underlying dynamics of a physical system has gained attraction in the past decade. Current approaches employ pre-specified functional forms or basis functions and often…
This work introduces an efficient novel approach for epistemic uncertainty estimation for ensemble models for regression tasks using pairwise-distance estimators (PaiDEs). Utilizing the pairwise-distance between model components, these…
Learning from heterogeneous data poses challenges such as combining data from various sources and of different types. Meanwhile, heterogeneous data are often associated with missingness in real-world applications due to heterogeneity and…
We develop a class of rules spanning the range between quadratic discriminant analysis and naive Bayes, through a path of sparse graphical models. A group lasso penalty is used to introduce shrinkage and encourage a similar pattern of…
We utilize extreme-learning machines for the prediction of partial differential equations (PDEs). Our method splits the state space into multiple windows that are predicted individually using a single model. Despite requiring only few data…
Adaptive sampling results in dramatic improvements in the recovery of sparse signals in white Gaussian noise. A sequential adaptive sampling-and-refinement procedure called Distilled Sensing (DS) is proposed and analyzed. DS is a form of…
Numerically solving partial differential equations (PDEs) can be challenging and computationally expensive. This has led to the development of reduced-order models (ROMs) that are accurate but faster than full order models (FOMs). Recently,…
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…
Many systems in physics, engineering, and biology exhibit multiscale stochastic dynamics, where low-dimensional slow variables evolve under the influence of high-dimensional fast processes. In practice, observations are often limited to a…
In many scientific studies, it becomes increasingly important to delineate the causal pathways through a large number of mediators, such as genetic and brain mediators. Structural equation modeling (SEM) is a popular technique to estimate…
We develop an all-at-once modeling framework for learning systems of ordinary differential equations (ODE) from scarce, partial, and noisy observations of the states. The proposed methodology amounts to a combination of sparse recovery…
Structuring the latent space in probabilistic deep generative models, e.g., variational autoencoders (VAEs), is important to yield more expressive models and interpretable representations, and to avoid overfitting. One way to achieve this…
Although sparse training has been successfully used in various resource-limited deep learning tasks to save memory, accelerate training, and reduce inference time, the reliability of the produced sparse models remains unexplored. Previous…