Search Results for « Deep Variational Bayes Filters »

These notes were compiled as lecture notes for a course developed and taught at the University of the Southern California. They should be accessible to a typical engineering graduate student with a strong background in Applied Mathematics. The main objective of these notes is to introduce a student who is familiar with concepts in linear algebra and partial differential equations to select topics in deep learning. These lecture notes exploit the strong connections between deep learning algorithms and the more conventional techniques of computational physics to achieve two goals. First, they use concepts from computational physics to develop an understanding of deep learning algorithms. Not surprisingly, many concepts in deep learning can be connected to similar concepts in computational physics, and one can utilize this connection to better understand these algorithms. Second, several novel deep learning algorithms can be used to solve challenging problems in computational physics. Thus, they offer someone who is interested in modeling a physical phenomena with a complementary set of tools.

We introduce Deep Variational Bayes Filters (DVBF), a new method for unsupervised learning and identification of latent Markovian state space models. Leveraging recent advances in Stochastic Gradient Variational Bayes, DVBF can overcome intractable inference distributions via variational inference. Thus, it can handle highly nonlinear input data with temporal and spatial dependencies such as image sequences without domain knowledge. Our experiments show that enabling backpropagation through transitions enforces state space assumptions and significantly improves information content of the latent embedding. This also enables realistic long-term prediction.

Deep Neural Networks, often owing to the overparameterization, are shown to be capable of exactly memorizing even randomly labelled data. Empirical studies have also shown that none of the standard regularization techniques mitigate such overfitting. We investigate whether the choice of the loss function can affect this memorization. We empirically show, with benchmark data sets MNIST and CIFAR-10, that a symmetric loss function, as opposed to either cross-entropy or squared error loss, results in significant improvement in the ability of the network to resist such overfitting. We then provide a formal definition for robustness to memorization and provide a theoretical explanation as to why the symmetric losses provide this robustness. Our results clearly bring out the role loss functions alone can play in this phenomenon of memorization.

The Finite Element Method (FEM) is a widely used technique for simulating crash scenarios with high accuracy and reliability. To reduce the significant computational costs associated with FEM, the Finite Element Method Integrated Networks (FEMIN) framework integrates neural networks (NNs) with FEM solvers. However, this integration can introduce errors and deviations from full-FEM simulations, highlighting the need for an additional metric to assess prediction confidence, especially when no ground truth data is available. In this study, we adapt the Deep Variational Bayes Filter (DVBF) to the FEMIN framework, incorporating a probabilistic approach to provide qualitative insights into prediction confidence during FEMIN simulations. The adaptation involves using the learned transition model for a predictive decoding step, generating a preliminary force prediction. This predictive force is used alongside the displacement and the velocity data from the FEM solver as input for the encoder model. The decoder reconstructs the likelihood distribution based on the posterior. The mean force of this distribution is applied to the FEM solver, while the predicted standard deviation can be used for uncertainty estimation. Our findings demonstrate that the DVBF outperforms deterministic NN architectures in terms of accuracy. Furthermore, the standard deviation derived from the decoder serves as a valuable qualitative metric for assessing the confidence in FEMIN simulations. This approach enhances the robustness of FEMIN by providing a measure of reliability alongside the simulation results.

Deep neural networks and the ENO procedure are both efficient frameworks for approximating rough functions. We prove that at any order, the ENO interpolation procedure can be cast as a deep ReLU neural network. This surprising fact enables the transfer of several desirable properties of the ENO procedure to deep neural networks, including its high-order accuracy at approximating Lipschitz functions. Numerical tests for the resulting neural networks show excellent performance for approximating solutions of nonlinear conservation laws and at data compression.

This paper addresses the estimation of trajectories of interacting vehicles at a microscopic scale, as a prerequisite to their prediction for risk assessment. A state-space solution is investigated, where both the Markov hidden state (continuous-valued, which captures the joint histories of vehicles) and the measurements (low-dimensional and noisy) admit a vehicle-wise structure. The vehicles' transition models are assumed independent of each other, time- and vehicle-invariant, and coequal to an “egocentric” prior dynamics pdf. To cope with the vehicles' interactions, this pdf is conditioned on the full state vector as the past time index, which imposes a centralized estimation/prediction of the fleet motion. The two fundamental pillars of the approach are developed: learning of a Gaussian mixture egocentric transition model by means of Deep Neural Networks; synthesis of a stochastic variational Bayes filtering algorithm which features a decentralized vehicle-wise structure but takes into account interactions. Tests on highway scenarios are presented.

Evidential deep learning, built upon belief theory and subjective logic, offers a principled and computationally efficient way to turn a deterministic neural network uncertainty-aware. The resultant evidential models can quantify fine-grained uncertainty using the learned evidence. To ensure theoretically sound evidential models, the evidence needs to be non-negative, which requires special activation functions for model training and inference. This constraint often leads to inferior predictive performance compared to standard softmax models, making it challenging to extend them to many large-scale datasets. To unveil the real cause of this undesired behavior, we theoretically investigate evidential models and identify a fundamental limitation that explains the inferior performance: existing evidential activation functions create zero evidence regions, which prevent the model to learn from training samples falling into such regions. A deeper analysis of evidential activation functions based on our theoretical underpinning inspires the design of a novel regularizer that effectively alleviates this fundamental limitation. Extensive experiments over many challenging real-world datasets and settings confirm our theoretical findings and demonstrate the effectiveness of our proposed approach.

Here we propose the reweighted autoencoded variational Bayes for enhanced sampling (RAVE) method, a new iterative scheme that uses the deep learning framework of variational autoencoders to enhance sampling in molecular simulations. RAVE involves iterations between molecular simulations and deep learning in order to produce an increasingly accurate probability distribution along a low-dimensional latent space that captures the key features of the molecular simulation trajectory. Using the Kullback-Leibler divergence between this latent space distribution and the distribution of various trial reaction coordinates sampled from the molecular simulation, RAVE determines an optimum, yet nonetheless physically interpretable, reaction coordinate and optimum probability distribution. Both then directly serve as the biasing protocol for a new biased simulation, which is once again fed into the deep learning module with appropriate weights accounting for the bias, the procedure continuing until estimates of desirable thermodynamic observables are converged. Unlike recent methods using deep learning for enhanced sampling purposes, RAVE stands out in that (a) it naturally produces a physically interpretable reaction coordinate, (b) is independent of existing enhanced sampling protocols to enhance the fluctuations along the latent space identified via deep learning, and (c) it provides the ability to easily filter out spurious solutions learned by the deep learning procedure. The usefulness and reliability of RAVE is demonstrated by applying it to model potentials of increasing complexity, including computation of the binding free energy profile for a hydrophobic ligand-substrate system in explicit water with dissociation time of more than 3 min, in computer time at least twenty times less than that needed for umbrella sampling or metadynamics.

We consider the generic deep image enhancement problem where an input image is transformed into a perceptually better-looking image. Recent methods for image enhancement consider the problem by performing style transfer and image restoration. The methods mostly fall into two categories: training data-based and training data-independent (deep internal learning methods). We perform image enhancement in the deep internal learning framework. Our Deep Internal Learning for Image Enhancement framework enhances content features and style features and uses contextual content loss for preserving image context in the enhanced image. We show results on both hazy and noisy image enhancement. To validate the results, we use structure similarity and perceptual error, which is efficient in measuring the unrealistic deformation present in the images. We show that the proposed framework outperforms the relevant state-of-the-art works for image enhancement.

System identification of complex and nonlinear systems is a central problem for model predictive control and model-based reinforcement learning. Despite their complexity, such systems can often be approximated well by a set of linear dynamical systems if broken into appropriate subsequences. This mechanism not only helps us find good approximations of dynamics, but also gives us deeper insight into the underlying system. Leveraging Bayesian inference, Variational Autoencoders and Concrete relaxations, we show how to learn a richer and more meaningful state space, e.g. encoding joint constraints and collisions with walls in a maze, from partial and high-dimensional observations. This representation translates into a gain of accuracy of learned dynamics showcased on various simulated tasks.