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We present a new deep primal-dual backward stochastic differential equation framework based on stopping time iteration to solve optimal stopping problems. A novel loss function is proposed to learn the conditional expectation, which…

Answer Set Programming (ASP) is a generic problem modeling and solving framework with a strong focus on knowledge representation and a rapid growth of industrial applications. So far, the study of complexity resulted in characterizing…

Long-term fluid dynamics forecasting is a critically important problem in science and engineering. While neural operators have emerged as a promising paradigm for modeling systems governed by partial differential equations (PDEs), they…

Rapid advances in data collection and processing capabilities have allowed for the use of increasingly complex models that give rise to nonconvex optimization problems. These formulations, however, can be arbitrarily difficult to solve in…

Simulation-based inference (SBI) enables parameter estimation for complex stochastic models with intractable likelihoods when model simulation is feasible. Neural posterior estimation (NPE) is a popular SBI approach that often achieves…

We consider a generic convex-concave saddle point problem with separable structure, a form that covers a wide-ranged machine learning applications. Under this problem structure, we follow the framework of primal-dual updates for saddle…

Maximum-a-posteriori (MAP) approaches are an effective framework for inverse problems with known forward operators, particularly when combined with expressive priors and careful parameter selection. In blind settings, however, their use…

In this work, we conduct the first systematic study of stochastic variational inequality (SVI) and stochastic saddle point (SSP) problems under the constraint of differential privacy (DP). We propose two algorithms: Noisy Stochastic…

Evaluation in scientific reconstruction is dominated by pointwise metrics - RMSE, MAE, per-event resolution - under the implicit assumption that lower error means better reconstruction. We show that this assumption fails structurally for…

We prove an existence and uniqueness result for two-obstacle problem for quasilinear Stochastic PDEs (DOSPDEs for short). The method is based on the probabilistic interpretation of the solution by using the backward doubly stochastic…

A systematic Bayesian framework is developed for physics constrained parameter inference ofstochastic differential equations (SDE) from partial observations. The physical constraints arederived for stochastic climate models but are…

Backward stochastic differential equation (BSDE) provides probabilistic solutions for a class of parabolic partial differential equations (PDEs). DeepBSDE and FBSNN are two deep learning approaches for solving high-dimensional PDEs through…

Although sparse training has been successfully used in various resource-limited deep learning tasks to save memory, accelerate training, and reduce inference time, the reliability of the produced sparse models remains unexplored. Previous…

Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical…

Motivated by Pryce's structural index reduction method for differential algebraic equations (DAEs), we show the complexity of the fixed-point iteration algorithm and propose a fixed-point iteration method with parameters. It leads to a…

A recent line of work shows that a deep neural network with ReLU nonlinearities arises from a finite sequence of cascaded sparse coding models, the outputs of which, except for the last element in the cascade, are sparse and unobservable.…

We present a model of roundoff error analysis that combines simplicity with predictive power. Though not considering all sources of roundoff within an algorithm, the model is related to a recursive roundoff error analysis and therefore…

Computing the Bayesian posterior of a neural network is a challenging task due to the high-dimensionality of the parameter space. Anchored ensembles approximate the posterior by training an ensemble of neural networks on anchored losses…

We address a numerical methodology for the computation of coarse-grained stable and unstable manifolds of saddle equilibria/stationary states of multiscale/stochastic systems for which a "good" macroscopic description in the form of…

We study bandit learning in matching markets with two-sided reward uncertainty, extending prior research primarily focused on single-sided uncertainty. Leveraging the concept of `super-stability' from Irving (1994), we demonstrate the…