Related papers: Symbolic Graph Networks for Robust PDE Discovery f…
The physical world is governed by the laws of physics, often represented in form of nonlinear partial differential equations (PDEs). Unfortunately, solution of PDEs is non-trivial and often involves significant computational time. With…
This work introduces a highly-scalable spectral graph densification framework (SGL) for learning resistor networks with linear measurements, such as node voltages and currents. We show that the proposed graph learning approach is equivalent…
The working mechanisms of complex natural systems tend to abide by concise and profound partial differential equations (PDEs). Methods that directly mine equations from data are called PDE discovery, which reveals consistent physical laws…
We present a novel model Graph Neural Stochastic Differential Equations (Graph Neural SDEs). This technique enhances the Graph Neural Ordinary Differential Equations (Graph Neural ODEs) by embedding randomness into data representation using…
Representing and exploiting multivariate signals requires capturing relations between variables, which we can represent by graphs. Graph dictionaries allow to describe complex relational information as a sparse sum of simpler structures,…
We introduce Graph-Structured Sum-Product Networks (GraphSPNs), a probabilistic approach to structured prediction for problems where dependencies between latent variables are expressed in terms of arbitrary, dynamic graphs. While many…
Signed Graph Neural Networks (SGNNs) have recently gained attention as an effective tool for several learning tasks on signed networks, i.e., graphs where edges have an associated polarity. One of these tasks is to predict the polarity of…
Graph neural networks are increasingly becoming the go-to approach in various fields such as computer vision, computational biology and chemistry, where data are naturally explained by graphs. However, unlike traditional convolutional…
In compressive sensing, a small collection of linear projections of a sparse signal contains enough information to permit signal recovery. Distributed compressive sensing (DCS) extends this framework by defining ensemble sparsity models,…
We develop a general approach to distill symbolic representations of a learned deep model by introducing strong inductive biases. We focus on Graph Neural Networks (GNNs). The technique works as follows: we first encourage sparse latent…
Sparse Identification of Nonlinear Dynamics (SINDy) is a method of system discovery that has been shown to successfully recover governing dynamical systems from data (Brunton et al., PNAS, '16; Rudy et al., Sci. Adv. '17). Recently, several…
Generative modeling of graphs with spatial structure is essential across many applications from computer graphics to spatial genomics. Recent flow-based generative models have achieved impressive results by gradually adding and then…
Physics-informed neural networks (PINNs) have successfully addressed various computational physics problems based on partial differential equations (PDEs). However, while tackling issues related to irregularities like singularities and…
Graph Neural Networks (GNN) exhibit superior performance in graph representation learning, but their inference cost can be high, due to an aggregation operation that can require a memory fetch for a very large number of nodes. This…
In complex physical systems, conventional differential equations often fall short in capturing non-local and memory effects, as they are limited to local dynamics and integer-order interactions. This study introduces a stepwise data-driven…
Noisy training set usually leads to the degradation of generalization and robustness of neural networks. In this paper, we propose using a theoretically guaranteed noisy label detection framework to detect and remove noisy data for Learning…
Heterogeneous networks, which connect informative nodes containing text with different edge types, are routinely used to store and process information in various real-world applications. Graph Neural Networks (GNNs) and their hyperbolic…
The study presents a general framework for discovering underlying Partial Differential Equations (PDEs) using measured spatiotemporal data. The method, called Sparse Spatiotemporal System Discovery ($\text{S}^3\text{d}$), decides which…
Modeling the traffic dynamics is essential for understanding and predicting the traffic spatiotemporal evolution. However, deriving the partial differential equation (PDE) models that capture these dynamics is challenging due to their…
In this paper, we propose a data-driven framework for model discovery of stochastic differential equations (SDEs) from a single trajectory, without requiring the ergodicity or stationary assumption on the underlying continuous process. By…