Designing optimal low-thrust gravity-assist trajectories using space-pruning and a multi-objective approach

A multi-objective problem is addressed consisting of finding optimal low-thrust gravity-assist trajectories for interplanetary and orbital transfers. For this, recently developed pruning techniques for incremental search space reduction - which will be extended for the current situation - in combination with subdivision techniques for the approximation of the entire solution set, the so-called Pareto set, are used. Subdivision techniques are particularly promising for the numerical treatment of these multi-objective design problems since they are characterized (amongst others) by highly disconnected feasible domains, which can easily be handled by these set oriented methods. The complexity of the novel pruning techniques is analysed, and finally the usefulness of the novel approach is demonstrated by showing some numerical results for two realistic cases

Satisfiability Modulo ODEs

We study SMT problems over the reals containing ordinary differential equations. They are important for formal verification of realistic hybrid systems and embedded software. We develop delta-complete algorithms for SMT formulas that are purely existentially quantified, as well as exists-forall formulas whose universal quantification is restricted to the time variables. We demonstrate scalability of the algorithms, as implemented in our open-source solver dReal, on SMT benchmarks with several hundred nonlinear ODEs and variables.Comment: Published in FMCAD 201

Learning to Prune Deep Neural Networks via Layer-wise Optimal Brain Surgeon

How to develop slim and accurate deep neural networks has become crucial for real- world applications, especially for those employed in embedded systems. Though previous work along this research line has shown some promising results, most existing methods either fail to significantly compress a well-trained deep network or require a heavy retraining process for the pruned deep network to re-boost its prediction performance. In this paper, we propose a new layer-wise pruning method for deep neural networks. In our proposed method, parameters of each individual layer are pruned independently based on second order derivatives of a layer-wise error function with respect to the corresponding parameters. We prove that the final prediction performance drop after pruning is bounded by a linear combination of the reconstructed errors caused at each layer. Therefore, there is a guarantee that one only needs to perform a light retraining process on the pruned network to resume its original prediction performance. We conduct extensive experiments on benchmark datasets to demonstrate the effectiveness of our pruning method compared with several state-of-the-art baseline methods

SCANN: Synthesis of Compact and Accurate Neural Networks

Deep neural networks (DNNs) have become the driving force behind recent artificial intelligence (AI) research. An important problem with implementing a neural network is the design of its architecture. Typically, such an architecture is obtained manually by exploring its hyperparameter space and kept fixed during training. This approach is time-consuming and inefficient. Another issue is that modern neural networks often contain millions of parameters, whereas many applications and devices require small inference models. However, efforts to migrate DNNs to such devices typically entail a significant loss of classification accuracy. To address these challenges, we propose a two-step neural network synthesis methodology, called DR+SCANN, that combines two complementary approaches to design compact and accurate DNNs. At the core of our framework is the SCANN methodology that uses three basic architecture-changing operations, namely connection growth, neuron growth, and connection pruning, to synthesize feed-forward architectures with arbitrary structure. SCANN encapsulates three synthesis methodologies that apply a repeated grow-and-prune paradigm to three architectural starting points. DR+SCANN combines the SCANN methodology with dataset dimensionality reduction to alleviate the curse of dimensionality. We demonstrate the efficacy of SCANN and DR+SCANN on various image and non-image datasets. We evaluate SCANN on MNIST and ImageNet benchmarks. In addition, we also evaluate the efficacy of using dimensionality reduction alongside SCANN (DR+SCANN) on nine small to medium-size datasets. We also show that our synthesis methodology yields neural networks that are much better at navigating the accuracy vs. energy efficiency space. This would enable neural network-based inference even on Internet-of-Things sensors.Comment: 13 pages, 8 figure