Related papers: Eigen-informed NeuralODEs: Dealing with stability …
Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. Here, we explore the use of Neural Ordinary Differential Equations, a recently introduced family of…
Recent advancements in artificial intelligence, particularly deep neural networks, have pushed the boundaries of what is achievable in complex tasks. Traditional methods for training neural networks in classification problems often rely on…
The overall performance or expected excess risk of an iterative machine learning algorithm can be decomposed into training error and generalization error. While the former is controlled by its convergence analysis, the latter can be tightly…
The numerical simulation and optimization of technical systems described by partial differential equations is expensive, especially in multi-query scenarios in which the underlying equations have to be solved for different parameters. A…
We propose a method for training ordinary differential equations by using a control-theoretic Lyapunov condition for stability. Our approach, called LyaNet, is based on a novel Lyapunov loss formulation that encourages the inference…
Neural networks are increasingly applied to support decision making in safety-critical applications (like autonomous cars, unmanned aerial vehicles and face recognition based authentication). While many impressive static verification…
Much as replacing hand-designed features with learned functions has revolutionized how we solve perceptual tasks, we believe learned algorithms will transform how we train models. In this work we focus on general-purpose learned optimizers…
Although neural operators are widely used in data-driven physical simulations, their training remains computationally expensive. Recent advances address this issue via downstream learning, where a model pretrained on simpler problems is…
Deep-learning-based methods for different applications have been shown vulnerable to adversarial examples. These examples make deployment of such models in safety-critical tasks questionable. Use of deep neural networks as inverse problem…
Recurrent neural networks (RNNs) are particularly well-suited for modeling long-term dependencies in sequential data, but are notoriously hard to train because the error backpropagated in time either vanishes or explodes at an exponential…
This work proposes a multimodal diffeomorphic registration method using Neural Ordinary Differential Equations (Neural ODEs). Nonrigid registration algorithms exhibit tradeoffs between their accuracy, the computational complexity of their…
The current learning process of deep learning, regardless of any deep neural network (DNN) architecture and/or learning algorithm used, is essentially a single resolution training. We explore multiresolution learning and show that…
A lack of software reproducibility has become increasingly apparent in the last several years, calling into question the validity of scientific findings affected by published tools. Reproducibility issues may have numerous sources of error,…
In data-driven modeling of spatiotemporal phenomena careful consideration often needs to be made in capturing the dynamics of the high wavenumbers. This problem becomes especially challenging when the system of interest exhibits shocks or…
In numerous robotics and mechanical engineering applications, among others, data is often constrained on smooth manifolds due to the presence of rotational degrees of freedom. Common datadriven and learning-based methods such as neural…
Over-parameterized neural network models often lead to significant performance discrepancies between training and test sets, a phenomenon known as overfitting. To address this, researchers have proposed numerous regularization techniques…
Many applications require the robustness, or ideally the invariance, of a neural network to certain transformations of input data. Most commonly, this requirement is addressed by either augmenting the training data, using adversarial…
High-precision scientific simulation faces a long-standing trade-off between computational efficiency and physical fidelity. To address this challenge, we propose NeuralOGCM, an ocean modeling framework that fuses differentiable programming…
We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary…
Continuous-time neural processes are performant sequential decision-makers that are built by differential equations (DE). However, their expressive power when they are deployed on computers is bottlenecked by numerical DE solvers. This…