相关论文: Random Controlled Differential Equations

We introduce a generative learning framework to model high-dimensional parametric systems using gradient guidance and virtual observations. We consider systems described by Partial Differential Equations (PDEs) discretized with structured…

We propose a deep signature/log-signature FBSDE algorithm to solve forward-backward stochastic differential equations (FBSDEs) with state and path dependent features. By incorporating the deep signature/log-signature transformation into the…

Often we wish to predict a large number of variables that depend on each other as well as on other observed variables. Structured prediction methods are essentially a combination of classification and graphical modeling, combining the…

Extensive research has produced robust methods for unsupervised data visualization. Yet supervised visualization$\unicode{x2013}$where expert labels guide representations$\unicode{x2013}$remains underexplored, as most supervised approaches…

Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…

While random Fourier features are a classic tool in kernel methods, their utility as a pre-processing step for deep learning on tabular data has been largely overlooked. Motivated by shortcomings in tabular deep learning pipelines -…

Two fundamental problems in unsupervised learning are efficient inference for latent-variable models and robust density estimation based on large amounts of unlabeled data. Algorithms for the two tasks, such as normalizing flows and…

Learning-based congestion control (CC), including Reinforcement-Learning, promises efficient CC in a fast-changing networking landscape, where evolving communication technologies, applications and traffic workloads pose severe challenges to…

Neural networks inspired by differential equations have proliferated for the past several years. Neural ordinary differential equations (NODEs) and neural controlled differential equations (NCDEs) are two representative examples of them. In…

Queuing network control is essential for managing congestion in job-processing systems such as service systems, communication networks, and manufacturing processes. Despite growing interest in applying reinforcement learning (RL)…

Forecasting atmospheric flows with traditional discretization methods, also called full order methods (e.g., finite element methods or finite volume methods), is computationally expensive. We propose to reduce the computational cost with a…

We investigate neural ordinary and stochastic differential equations (neural ODEs and SDEs) to model stochastic dynamics in fully and partially observed environments within a model-based reinforcement learning (RL) framework. Through a…

Modelling partial differential equations (PDEs) is of crucial importance in science and engineering, and it includes tasks ranging from forecasting to inverse problems, such as data assimilation. However, most previous numerical and machine…

The conjoining of dynamical systems and deep learning has become a topic of great interest. In particular, neural differential equations (NDEs) demonstrate that neural networks and differential equation are two sides of the same coin.…

Continuous-depth neural networks, such as the Neural Ordinary Differential Equations (ODEs), have aroused a great deal of interest from the communities of machine learning and data science in recent years, which bridge the connection…

Often the analysis of time-dependent chemical and biophysical systems produces high-dimensional time-series data for which it can be difficult to interpret which individual features are most salient. While recent work from our group and…

The success of Transformer-based models has encouraged many researchers to learn CAD models using sequence-based approaches. However, learning CAD models is still a challenge, because they can be represented as complex shapes with long…

Clustering single-cell RNA sequence (scRNA-seq) data poses statistical and computational challenges due to their high-dimensionality and data-sparsity, also known as `dropout' events. Recently, Regularized Auto-Encoder (RAE) based deep…

Time-series data in real-world medical settings typically exhibit long-range dependencies and are observed at non-uniform intervals. In such contexts, traditional sequence-based recurrent models struggle. To overcome this, researchers…

This paper presents a computationally efficient approach for robust Model Predictive Control of nonlinear systems by combining Random Fourier Features with tube-based MPC. Tube-based Model Predictive Control provides robust constraint…