Related papers: Neural network augmented inverse problems for PDEs

An accurate impact parameter determination in a heavy ion collision is crucial for almost all further analysis. The capabilities of an artificial neural network are investigated to that respect. A novel input generation for the network is…

Neural networks and Gaussian processes are complementary in their strengths and weaknesses. Having a better understanding of their relationship comes with the promise to make each method benefit from the strengths of the other. In this…

Deep Neural Networks (DNNs) are powerful tools for various computer vision tasks, yet they often struggle with reliable uncertainty quantification - a critical requirement for real-world applications. Bayesian Neural Networks (BNN) are…

Statistical methods such as the Box-Jenkins method for time-series forecasting have been prominent since their development in 1970. Many researchers rely on such models as they can be efficiently estimated and also provide interpretability.…

Recent studies have shown that Convolutional Neural Networks (CNNs) are vulnerable to a small perturbation of input called "adversarial examples". In this work, we propose a new feedforward CNN that improves robustness in the presence of…

We explore in detail a method to solve ordinary differential equations using feedforward neural networks. We prove a specific loss function, which does not require knowledge of the exact solution, to be a suitable standard metric to…

Solving inverse problems in physics is central to understanding complex systems and advancing technologies in various fields. Iterative optimization algorithms, commonly used to solve these problems, often encounter local minima, chaos, or…

We propose an end-to-end model based on convolutional and recurrent neural networks for speech enhancement. Our model is purely data-driven and does not make any assumptions about the type or the stationarity of the noise. In contrast to…

We study the problem of computing the preimage of a set under a neural network with piecewise-affine activation functions. We recall an old result that the preimage of a polyhedral set is again a union of polyhedral sets and can be…

One approach to deal with the statistical inefficiency of neural networks is to rely on auxiliary losses that help to build useful representations. However, it is not always trivial to know if an auxiliary task will be helpful for the main…

Solving nonlinear partial differential equations (PDEs) with multiple solutions using neural networks has found widespread applications in various fields such as physics, biology, and engineering. However, classical neural network methods…

Solving inverse problems with neural networks benefits from very few theoretical guarantees when it comes to the recovery guarantees. We provide in this work convergence and recovery guarantees for self-supervised neural networks applied to…

We introduce NoisyNet, a deep reinforcement learning agent with parametric noise added to its weights, and show that the induced stochasticity of the agent's policy can be used to aid efficient exploration. The parameters of the noise are…

The data consistency for the physical forward model is crucial in inverse problems, especially in MR imaging reconstruction. The standard way is to unroll an iterative algorithm into a neural network with a forward model embedded. The…

Recent works have shown that deep neural networks can be employed to solve partial differential equations, giving rise to the framework of physics informed neural networks. We introduce a generalization for these methods that manifests as a…

Neural networks are very successful at detecting patterns in noisy data, and have become the technology of choice in many fields. However, their usefulness is hampered by their susceptibility to adversarial attacks. Recently, many methods…

This paper proposes a new framework using physics-informed neural networks (PINNs) to simulate complex structural systems that consist of single and double beams based on Euler-Bernoulli and Timoshenko theory, where the double beams are…

With neural networks being used to control safety-critical systems, they increasingly have to be both accurate (in the sense of matching inputs to outputs) and robust. However, these two properties are often at odds with each other and a…

We explore the robustness of recurrent neural networks when the computations within the network are noisy. One of the motivations for looking into this problem is to reduce the high power cost of conventional computing of neural network…

The topology of artificial neural networks has a significant effect on their performance. Characterizing efficient topology is a field of promising research in Artificial Intelligence. However, it is not a trivial task and it is mainly…