Related papers: Index-aware learning of circuits
The discovery of partial differential equations (PDEs) is a challenging task that involves both theoretical and empirical methods. Machine learning approaches have been developed and used to solve this problem; however, it is important to…
The complexity of real-world geophysical systems is often compounded by the fact that the observed measurements depend on hidden variables. These latent variables include unresolved small scales and/or rapidly evolving processes, partially…
Power system dynamics are generally modeled by high dimensional nonlinear differential-algebraic equations (DAEs) given a large number of components forming the network. These DAEs' complexity can grow exponentially due to the increasing…
Power system dynamics are generally modeled by high dimensional nonlinear differential-algebraic equations (DAEs) given a large number of components forming the network. These DAEs' complexity can grow exponentially due to the increasing…
Graph embedding algorithms are used to efficiently represent (encode) a graph in a low-dimensional continuous vector space that preserves the most important properties of the graph. One aspect that is often overlooked is whether the graph…
Causal learning from data has received much attention recently. Bayesian networks can be used to capture causal relationships. There, one recovers a weighted directed acyclic graph in which random variables are represented by vertices, and…
The data-driven recovery of the unknown governing equations of dynamical systems has recently received an increasing interest. However, the identification of governing equations remains challenging when dealing with noisy and partial…
A widely used strategy to discover and understand language model mechanisms is circuit analysis. A circuit is a minimal subgraph of a model's computation graph that executes a specific task. We identify a gap in existing circuit discovery…
Learning disentanglement aims at finding a low dimensional representation which consists of multiple explanatory and generative factors of the observational data. The framework of variational autoencoder (VAE) is commonly used to…
Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multi-scale physics in a compact and symbolic representation. This…
As digitization in engineering progressed, circuit diagrams (also referred to as schematics) are typically developed and maintained in computer-aided engineering (CAE) systems, thus allowing for automated verification, simulation and…
In recent years, extending variational autoencoder's framework to learn disentangled representations has received much attention. We address this problem by proposing a framework capable of disentangling class-related and class-independent…
Feature engineering, a crucial step of machine learning, aims to extract useful features from raw data to improve data quality. In recent years, great efforts have been devoted to Automated Feature Engineering (AutoFE) to replace expensive…
Directed acyclic graphs (DAGs) with hidden variables are often used to characterize causal relations between variables in a system. When some variables are unobserved, DAGs imply a notoriously complicated set of constraints on the…
The laws of physics have been written in the language of dif-ferential equations for centuries. Neural Ordinary Differen-tial Equations (NODEs) are a new machine learning architecture which allows these differential equations to be learned…
Learning Interpretable representation in medical applications is becoming essential for adopting data-driven models into clinical practice. It has been recently shown that learning a disentangled feature representation is important for a…
Data-driven discovery of "hidden physics" -- i.e., machine learning of differential equation models underlying observed data -- has recently been approached by embedding the discovery problem into a Gaussian Process regression of spatial…
As is well known, differential algebraic equations (DAEs), which are able to describe dynamic changes and underlying constraints, have been widely applied in engineering fields such as fluid dynamics, multi-body dynamics, mechanical systems…
Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…
We study linear abstract differential-algebraic equations (ADAEs), and we introduce an index concept which is based on polynomial growth of a~pseudo-resolvent. Our approach to solvability analysis is based on degenerate semigroups. We apply…