Related papers: Index-aware learning of circuits
In many applications, one needs to learn a dynamical system from its solutions sampled at a finite number of time points. The learning problem is often formulated as an optimization problem over a chosen function class. However, in the…
Although a number of related algorithms have been developed to evaluate influence diagrams, exploiting the conditional independence in the diagram, the exact solution has remained intractable for many important problems. In this paper we…
Learning interpretable representations with variational autoencoders (VAEs) is a major goal of representation learning. The main challenge lies in obtaining disentangled representations, where each latent dimension corresponds to a distinct…
To date, most discoveries of network subcomponents that implement human-interpretable computations in deep vision models have involved close study of single units and large amounts of human labor. We explore scalable methods for extracting…
The $\Sigma$-method for structural analysis of a differential-algebraic equation (DAE) system produces offset vectors from which the sparsity pattern of a system Jacobian is derived. This pattern implies a block-triangular form (BTF) of the…
We extend the scope of differential machine learning and introduce a new breed of supervised principal component analysis to reduce dimensionality of Derivatives problems. Applications include the specification and calibration of pricing…
Rapidly developing machine learning methods has stimulated research interest in computationally reconstructing differential equations (DEs) from observational data which may provide additional insight into underlying causative mechanisms.…
Traditional physics-informed neural networks (PINNs) do not always satisfy physics based constraints, especially when the constraints include differential operators. Rather, they minimize the constraint violations in a soft way. Strict…
Several algorithms in computer algebra involve the computation of a power series solution of a given ordinary differential equation. Over finite fields, the problem is often lifted in an approximate $p$-adic setting to be well-posed. This…
Spurred by tremendous success in pattern matching and prediction tasks, researchers increasingly resort to machine learning to aid original scientific discovery. Given large amounts of observational data about a system, can we uncover the…
Reachability analysis is a fundamental problem for safety verification and falsification of Cyber-Physical Systems (CPS) whose dynamics follow physical laws usually represented as differential equations. In the last two decades, numerous…
Learning the structure of dependence relations between variables is a pervasive issue in the statistical literature. A directed acyclic graph (DAG) can represent a set of conditional independences, but different DAGs may encode the same set…
The numerical solution of partial differential equations (PDEs) is challenging because of the need to resolve spatiotemporal features over wide length and timescales. Often, it is computationally intractable to resolve the finest features…
Variational Auto-Encoders (VAEs) are capable of learning latent representations for high dimensional data. However, due to the i.i.d. assumption, VAEs only optimize the singleton variational distributions and fail to account for the…
Although mechanism-based interpretability has generated an abundance of insight for discriminative network analysis, generative models are less understood -- particularly outside of image-related applications. We investigate how much of the…
We view disentanglement learning as discovering an underlying structure that equivariantly reflects the factorized variations shown in data. Traditionally, such a structure is fixed to be a vector space with data variations represented by…
We study the problem of reducing test-time acquisition costs in classification systems. Our goal is to learn decision rules that adaptively select sensors for each example as necessary to make a confident prediction. We model our system as…
A new method for learning variational autoencoders (VAEs) is developed, based on Stein variational gradient descent. A key advantage of this approach is that one need not make parametric assumptions about the form of the encoder…
Modern modeling languages for general physical systems, such as Modelica, Amesim, or Simscape, rely on Differential Algebraic Equations (DAE), i.e., constraints of the form f(dot{x},x,u)=0. This drastically facilitates modeling from first…
Anomaly detection is a well-established field in machine learning, identifying observations that deviate from typical patterns. The principles of anomaly detection could enhance our understanding of how biological systems recognize and…