Related papers: Positive concave deep equilibrium models

We develop a methodology that utilizes deep learning to simultaneously solve and estimate canonical continuous-time general equilibrium models in financial economics. We illustrate our method in two examples: (1) industrial dynamics of…

In this paper, we explore point-cloud based deep learning models to analyze numerical simulations arising from finite element analysis. The objective is to classify automatically the results of the simulations without tedious human…

Physics-Informed Neural Networks (PINNs) have aroused great attention for its ability to address forward and inverse problems of partial differential equations. However, approximating discontinuous functions by neural networks poses a…

Robust optimization has been established as a leading methodology to approach decision problems under uncertainty. To derive a robust optimization model, a central ingredient is to identify a suitable model for uncertainty, which is called…

We consider Nash-Cournot oligopolistic equilibrium models involving separable concave cost functions. In contrast to the models with linear and convex cost functions, in these models a local equilibrium point may not be a global one. We…

Recent work introduced a robust computational framework combining embedded mathematical structures, advanced optimization, and neural network architecture, leading to the discovery of multiple unstable self-similar solutions for key fluid…

Deep-predictive-coding networks (DPCNs) are hierarchical, generative models. They rely on feed-forward and feed-back connections to modulate latent feature representations of stimuli in a dynamic and context-sensitive manner. A crucial…

Stability is a fundamental property of dynamical systems, yet to this date it has had little bearing on the practice of recurrent neural networks. In this work, we conduct a thorough investigation of stable recurrent models. Theoretically,…

We present a lightweighted neural PDE representation to discover the hidden structure and predict the solution of different nonlinear PDEs. Our key idea is to leverage the prior of ``translational similarity'' of numerical PDE differential…

Deep neural networks, in particular convolutional neural networks, have become highly effective tools for compressing images and solving inverse problems including denoising, inpainting, and reconstruction from few and noisy measurements.…

Most algorithms for solving optimization problems or finding saddle points of convex-concave functions are fixed-point algorithms. In this work we consider the generic problem of finding a fixed point of an average of operators, or an…

Neural PDE solvers offer a powerful tool for modeling complex dynamical systems, but often struggle with error accumulation over long time horizons and maintaining stability and physical consistency. We introduce a multiscale implicit…

With recent advancements in deep learning methods, automatically learning deep features from the original data is becoming an effective and widespread approach. However, the hand-crafted expert knowledge-based features are still insightful.…

Backpropagation algorithm is indispensable for the training of feedforward neural networks. It requires propagating error gradients sequentially from the output layer all the way back to the input layer. The backward locking in…

Operator learning enables fast surrogate modeling of high-dimensional dynamical systems, but existing approaches face two fundamental limitations: quadratic inference complexity and unreliable uncertainty quantification in safety-critical…

Deep Learning is a consolidated, state-of-the-art Machine Learning tool to fit a function when provided with large data sets of examples. However, in regression tasks, the straightforward application of Deep Learning models provides a point…

Implicit deep learning has recently gained popularity with applications ranging from meta-learning to Deep Equilibrium Networks (DEQs). In its general formulation, it relies on expressing some components of deep learning pipelines…

In recent years, deep learning techniques have shown great success in various tasks related to inverse problems, where a target quantity of interest can only be observed through indirect measurements by a forward operator. Common approaches…

This paper introduces a new modeling framework for optimization under uncertainty, called Probable Event Constrained Optimization (PECO). Unlike conventional chance-constrained formulations, which only limit the probability of constraint…

Time-dependent partial differential equations (PDEs) are ubiquitous in science and engineering. Recently, mostly due to the high computational cost of traditional solution techniques, deep neural network based surrogates have gained…