Related papers: Implementation and (Inverse Modified) Error Analys…

The combination of numerical integration and deep learning, i.e., ODE-net, has been successfully employed in a variety of applications. In this work, we introduce inverse modified differential equations (IMDE) to contribute to the behaviour…

The combination of ordinary differential equations and neural networks, i.e., neural ordinary differential equations (Neural ODE), has been widely studied from various angles. However, deciphering the numerical integration in Neural ODE is…

Along with the practical success of the discovery of dynamics using deep learning, the theoretical analysis of this approach has attracted increasing attention. Prior works have established the grid error estimation with auxiliary…

Inverse problems are pervasive mathematical methods in inferring knowledge from observational and experimental data by leveraging simulations and models. Unlike direct inference methods, inverse problem approaches typically require many…

Random ordinary differential equations (RODEs), i.e. ODEs with random parameters, are often used to model complex dynamics. Most existing methods to identify unknown governing RODEs from observed data often rely on strong prior knowledge.…

The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. A central challenge in this setting is backpropagation through the solution of an…

Implicit layer deep learning techniques, like Neural Differential Equations, have become an important modeling framework due to their ability to adapt to new problems automatically. Training a neural differential equation is effectively a…

Differential equations in general and neural ODEs in particular are an essential technique in continuous-time system identification. While many deterministic learning algorithms have been designed based on numerical integration via the…

Classical neural ODEs trained with explicit methods are intrinsically limited by stability, crippling their efficiency and robustness for stiff learning problems that are common in graph learning and scientific machine learning. We present…

Learning models of dynamical systems with external inputs, which may be, for example, nonsmooth or piecewise, is crucial for studying complex phenomena and predicting future state evolution, which is essential for applications such as…

Deep learning based methods hold state-of-the-art results in low-level image processing tasks, but remain difficult to interpret due to their black-box construction. Unrolled optimization networks present an interpretable alternative to…

The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. A central challenge in this setting is backpropagation through the solution of an…

Many training data attribution (TDA) methods aim to estimate how a model's behavior would change if one or more data points were removed from the training set. Methods based on implicit differentiation, such as influence functions, can be…

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…

It has long been hoped that model-based control will improve tracking performance while maintaining or increasing compliance. This hope hinges on having or being able to estimate an accurate inverse dynamics model. As a result, substantial…

Anomaly detection (AD) is increasingly recognized as a key component for ensuring the resilience of future communication systems. While deep learning has shown state-of-the-art AD performance, its application in critical systems is hindered…

We propose a data-driven framework for learning reduced-order moment dynamics from PDE-governed systems using Neural ODEs. In contrast to derivative-based methods like SINDy, which necessitate densely sampled data and are sensitive to…

Design and optimal control problems are among the fundamental, ubiquitous tasks we face in science and engineering. In both cases, we aim to represent and optimize an unknown (black-box) function that associates a performance/outcome to a…

Neural networks have emerged as powerful tools across various applications, yet their decision-making process often remains opaque, leading to them being perceived as "black boxes." This opacity raises concerns about their interpretability…

Deep learning systems are known to exhibit implicit regularization (alt. implicit bias), favoring simple solutions instead of merely minimizing the loss function. In some cases, we can analytically derive the implicit regularization --…