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We study the problem of learning neural network models for Ordinary Differential Equations (ODEs) with parametric uncertainties. Such neural network models capture the solution to the ODE over a given set of parameters, initial conditions, and range of times. Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for learning such models that combine data-driven deep learning with symbolic physics models in a principled manner. However, the accuracy of PINNs degrade when they are used to solve an entire family of initial value problems characterized by varying parameters and initial conditions. In this paper, we combine symbolic differentiation and Taylor series methods to propose a class of higher-order models for capturing the solutions to ODEs. These models combine neural networks and symbolic terms: they use higher order Lie derivatives and a Taylor series expansion obtained symbolically, with the remainder term modeled as a neural network. The key insight is that the remainder term can itself be modeled as a solution to a first-order ODE. We show how the use of these higher order PINNs can improve accuracy using interesting, but challenging ODE benchmarks. We also show that the resulting model can be quite useful for situations such as controlling uncertain physical systems modeled as ODEs. 

We study the problem of out-of-distribution (OOD) detection, that is, detecting whether a machine learning (ML) model's output can be trusted at inference time. While a number of tests for OOD detection have been proposed in prior work, a formal framework for studying this problem is lacking. We propose a definition for the notion of OOD that includes both the input distribution and the ML model, which provides insights for the construction of powerful tests for OOD detection. We also propose a multiple hypothesis testing inspired procedure to systematically combine any number of different statistics from the ML model using conformal p-values. We further provide strong guarantees on the probability of incorrectly classifying an in-distribution sample as OOD. In our experiments, we find that threshold-based tests proposed in prior work perform well in specific settings, but not uniformly well across different OOD instances. In contrast, our proposed method that combines multiple statistics performs uniformly well across different datasets and neural networks architectures. 

This paper presents an approach to detect out-of-context (OOC) objects in an image. Given an image with a set of objects, our goal is to determine if an object is inconsistent with the scene context and detect the OOC object with a bounding box. In this work, we consider commonly explored contextual relations such as co-occurrence relations, the relative size of an object with respect to other objects, and the position of the object in the scene. We posit that contextual cues are useful to determine object labels for in-context objects and inconsistent context cues are detrimental to determining object labels for out-of-context objects. To realize this hypothesis, we propose a graph contextual reasoning network (GCRN) to detect OOC objects. GCRN consists of two separate graphs to predict object labels based on the contextual cues in the image: 1) a representation graph to learn object features based on the neighboring objects and 2) a context graph to explicitly capture contextual cues from the neighboring objects. GCRN explicitly captures the contextual cues to improve the detection of in-context objects and identify objects that violate contextual relations. In order to evaluate our approach, we create a large-scale dataset by adding OOC object instances to the COCO images. We also evaluate on recent OCD benchmark. Our results show that GCRN outperforms competitive baselines in detecting OOC objects and correctly detecting in-context objects. 

Deep neural networks (DNNs) have achieved near-human level accuracy on many datasets across different domains. But they are known to produce incorrect predictions with high confidence on inputs far from the training distribution. This challenge of lack of calibration of DNNs has limited the adoption of deep learning models in high-assurance systems such as autonomous driving, air traffic management, cybersecurity, and medical diagnosis. The problem of detecting when an input is outside the training distribution of a machine learning model, and hence, its prediction on this input cannot be trusted, has received significant attention recently. Several techniques based on statistical, geometric, topological, or relational signatures have been developed to detect the out-of-distribution (OOD) or novel inputs. In this paper, we present a runtime monitor based on predictive processing and dual process theory. We posit that the bottom-up deep neural networks can be monitored using top-down context models comprising two layers. The first layer is a feature density model that learns the joint distribution of the original DNN’s inputs, outputs, and the model’s explanation for its decisions. The second layer is a graph Markov neural network that captures an even broader context. We demonstrate the efficacy of our monitoring architecture in recognizing out-of-distribution and out-of-context inputs on the image classification and object detection tasks. 

Dataset accompanying code and paper: AircraftVerse: A Large-Scale Multimodal Dataset of Aerial Vehicle Designs We present AircraftVerse, a publicly available aerial vehicle design dataset. AircraftVerse contains 27,714 diverse battery powered aircraft designs that have been evaluated using state-of-the-art physics models that characterize performance metrics such as maximum flight distance and hover-time. This repository contains: A zip file "AircraftVerse.zip", where each design_X contains: design_tree.json: The design tree describes the design topology, choice of propulsion and energy subsystems. The tree also contains continuous parameters such as wing span, wing chord and arm length.design_seq.json: A preorder traversal of the design tree and store this as design_seq.json.design_low_level.json: The most low level representation of the design. This low level representation includes significant repetition that is avoided in the tree representation through the use of symmetry.Geom.stp: CAD design for the Aircraft in composition STP format (ISO 10303 standard).cadfile.stl: CAD design for the Aircraft in stereolithographic STL file,output.json: Summary containing the UAV's performance metrics such as maximum flight distance, maximum hover time, fight distance at maximum speed, maximum current draw, and mass.trims.npy: Contains the [Distance, Flight Time, Pitch, Control Input, Thrust, Lift, Drag, Current, Power] at each evaluated trim state (velocity).pointCloud.npy: Numpy array containing the corresponding point clouds for each design. corpus_dic: The corpus of components (e.g. batteries, propellers) that make up all aircraft designs. It is structured as a dictionary of dictionaries, with the high level components: ['Servo', 'GPS', 'ESC', 'Wing', 'Sensor', 'Propeller', 'Receiver', 'Motor', 'Battery', 'Autopilot'], containing a list of dictionaries corresponding to the component type. E.g. corpus_dic['Battery']['TurnigyGraphene2200mAh3S75C'] contains the detail of this particular battery. Corresponding code for this work is included at https://github.com/SRI-CSL/AircraftVerse.  Acknowledgements: This material is based upon work supported by the United States Air Force and DARPA under Contract No. FA8750-20-C-0002.  Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the United States Air Force and DARPA.   

Several methods have recently been developed for computing attributions of a neural network's prediction over the input features. However, these existing approaches for computing attributions are noisy and not robust to small perturbations of the input. This paper uses the recently identified connection between dynamical systems and residual neural networks to show that the attributions computed over neural stochastic differential equations (SDEs) are less noisy, visually sharper, and quantitatively more robust. Using dynamical systems theory, we theoretically analyze the robustness of these attributions. We also experimentally demonstrate the efficacy of our approach in providing smoother, visually sharper and quantitatively robust attributions by computing attributions for ImageNet images using ResNet-50, WideResNet-101 models and ResNeXt-101 models.