Related papers: EqOD: Symmetry-Informed Stability Selection for PD…

Identifying parameters in partial differential equations (PDEs) represents a very broad class of applied inverse problems. In recent years, several unsupervised learning approaches using (deep) neural networks have been developed to solve…

Variational quantum algorithms are promising for near-term quantum computing, but are severely limited by hardware noise and the substantial circuit overhead required for error mitigation methods such as Zero-Noise Extrapolation (ZNE). We…

Solving partial differential equations (PDEs) with machine learning typically requires training a new neural network for every new equation. This optimization is slow. We introduce MetaColloc. It is an optimization-free and data-free…

Sparse model identification enables the discovery of nonlinear dynamical systems purely from data; however, this approach is sensitive to noise, especially in the low-data limit. In this work, we leverage the statistical approach of…

Time-series anomaly detectors are commonly compared on workstation-class hardware under unconstrained execution. In-vehicle monitoring, however, requires predictable latency and stable behavior under limited CPU parallelism. Accuracy-only…

Recent research has observed that in machine learning optimization, gradient descent (GD) often operates at the edge of stability (EoS) [Cohen, et al., 2021], where the stepsizes are set to be large, resulting in non-monotonic losses…

We construct the first rigorously justified probabilistic algorithm for recovering the solution operator of a hyperbolic partial differential equation (PDE) in two variables from input-output training pairs. The primary challenge of…

Weakly supervised object detection (WSOD) focuses on training object detector with only image-level annotations, and is challenging due to the gap between the supervision and the objective. Most of existing approaches model WSOD as a…

We address the problem of predicting the next state of a dynamical system governed by unknown temporal partial differential equations (PDEs) using only a short trajectory. While standard transformers provide a natural black-box solution to…

Quantum error correction offers a promising path to suppress errors in quantum processors, but the resources required to protect logical operations from noise, especially non-Clifford operations, pose a substantial challenge to achieve…

We present a scalable, data-driven simulation framework for large-scale heating, ventilation, and air conditioning (HVAC) systems that couples physics-informed neural ordinary differential equations (PINODEs) with differential-algebraic…

We discover restrained numerical instabilities in current training practices of deep networks with stochastic gradient descent (SGD), and its variants. We show numerical error (on the order of the smallest floating point bit and thus the…

We evaluate the robustness of a probabilistic formulation of system identification (ID) to sparse, noisy, and indirect data. Specifically, we compare estimators of future system behavior derived from the Bayesian posterior of a learning…

We propose a nonlinear reduced basis method for the efficient approximation of parametrized partial differential equations (PDEs), exploiting kernel proper orthogonal decomposition (KPOD) for the generation of a reduced-order space and…

Deep learning experiments by Cohen et al. [2021] using deterministic Gradient Descent (GD) revealed an Edge of Stability (EoS) phase when learning rate (LR) and sharpness (i.e., the largest eigenvalue of Hessian) no longer behave as in…

In this paper, we introduce the Spectral Coefficient Learning via Operator Network (SCLON), a novel operator learning-based approach for solving parametric partial differential equations (PDEs) without the need for data harnessing. The…

Cyber-physical systems (CPS) like autonomous vehicles, that utilize learning components, are often sensitive to noise and out-of-distribution (OOD) instances encountered during runtime. As such, safety critical tasks depend upon OOD…

Threshold estimation is central to fault-tolerant quantum computing, but the reported threshold depends not only on the code and noise model, but also on the decoder used to interpret syndrome data. We study this dependence for surface-code…

Out-of-distribution (OOD) detection is critical for preventing deep learning models from making incorrect predictions to ensure the safety of artificial intelligence systems. Especially in safety-critical applications such as medical…

The increasing adoption of approximate computing in deep neural network accelerators (AxDNNs) promises significant energy efficiency gains. However, permanent faults in AxDNNs can severely degrade their performance compared to their…