Related papers: Power Series Expansion Neural Network
Power series are introduced that are simultaneously convergent for all real and p-adic numbers. Our expansions are in some aspects similar to those of exponential, trigonometric, and hyperbolic functions. Starting from these series and…
Adoption of deep neural networks in fields such as economics or finance has been constrained by the lack of interpretability of model outcomes. This paper proposes a generative neural network architecture - the parameter encoder neural…
Probabilistic power flow (PPF) plays a critical role in power system analysis. However, the high computational burden makes it challenging for the practical implementation of PPF. This paper proposes a model-based deep learning approach to…
Recent advances in statistical inference have significantly expanded the toolbox of probabilistic modeling. Historically, probabilistic modeling has been constrained to (i) very restricted model classes where exact or approximate…
We present Causal Posterior Estimation (CPE), a novel method for Bayesian inference in simulator models, i.e., models where the evaluation of the likelihood function is intractable or too computationally expensive, but where one can…
The expressive power of neural networks is important for understanding deep learning. Most existing works consider this problem from the view of the depth of a network. In this paper, we study how width affects the expressiveness of neural…
In this work we demonstrate the efficacy of neural networks in the characterization of dispersive media. We also develop a neural network to make predictions for input probe pulses which propagate through a nonlinear dispersive medium,…
This paper presents the Tensor Product Network (TPNet), a novel neural architecture for efficient and accurate function approximation and PDE solving. The core of the proposal involves constructing the solution explicitly as a linear…
This work presents the current collection of mathematical models related to neural networks and proposes a new family of such with extended structure and dynamics in order to attain a selection of cognitive capabilities. It starts by…
We extend Neural Processes (NPs) to sequential data through Recurrent NPs or RNPs, a family of conditional state space models. RNPs model the state space with Neural Processes. Given time series observed on fast real-world time scales but…
Deep neural networks are gaining in popularity as they are used to generate state-of-the-art results for a variety of computer vision and machine learning applications. At the same time, these networks have grown in depth and complexity in…
This paper presents a new neural network (NN) paradigm for scalable and generalizable stability analysis of power systems. The paradigm consists of two parts: the neural stability descriptor and the sample-augmented iterative training…
With the latest advances in Deep Learning-based generative models, it has not taken long to take advantage of their remarkable performance in the area of time series. Deep neural networks used to work with time series heavily depend on the…
The importance and cost of time-domain simulations when studying power systems have exponentially increased in the last decades. With the growing share of renewable energy sources, the slow and predictable responses from large turbines are…
More and more empirical and theoretical evidence shows that deepening neural networks can effectively improve their performance under suitable training settings. However, deepening the backbone of neural networks will inevitably and…
We investigate the complexity of deep neural networks through the lens of functional equivalence, which posits that different parameterizations can yield the same network function. Leveraging the equivalence property, we present a novel…
Deep convolutional neural networks have proven to be well suited for image classification applications. However, if there is distortion in the image, the classification accuracy can be significantly degraded, even with state-of-the-art…
Families of mixtures of multivariate power exponential (MPE) distributions have been previously introduced and shown to be competitive for cluster analysis in comparison to other elliptical mixtures including mixtures of Gaussian…
Neural networks have dramatically increased our capacity to learn from large, high-dimensional datasets across innumerable disciplines. However, their decisions are not easily interpretable, their computational costs are high, and building…
Recent studies have revealed the vulnerability of deep neural networks: A small adversarial perturbation that is imperceptible to human can easily make a well-trained deep neural network misclassify. This makes it unsafe to apply neural…