13,645 research outputs found
Formal Verification of Neural Network Controlled Autonomous Systems
In this paper, we consider the problem of formally verifying the safety of an
autonomous robot equipped with a Neural Network (NN) controller that processes
LiDAR images to produce control actions. Given a workspace that is
characterized by a set of polytopic obstacles, our objective is to compute the
set of safe initial conditions such that a robot trajectory starting from these
initial conditions is guaranteed to avoid the obstacles. Our approach is to
construct a finite state abstraction of the system and use standard
reachability analysis over the finite state abstraction to compute the set of
the safe initial states. The first technical problem in computing the finite
state abstraction is to mathematically model the imaging function that maps the
robot position to the LiDAR image. To that end, we introduce the notion of
imaging-adapted sets as partitions of the workspace in which the imaging
function is guaranteed to be affine. We develop a polynomial-time algorithm to
partition the workspace into imaging-adapted sets along with computing the
corresponding affine imaging functions. Given this workspace partitioning, a
discrete-time linear dynamics of the robot, and a pre-trained NN controller
with Rectified Linear Unit (ReLU) nonlinearity, the second technical challenge
is to analyze the behavior of the neural network. To that end, we utilize a
Satisfiability Modulo Convex (SMC) encoding to enumerate all the possible
segments of different ReLUs. SMC solvers then use a Boolean satisfiability
solver and a convex programming solver and decompose the problem into smaller
subproblems. To accelerate this process, we develop a pre-processing algorithm
that could rapidly prune the space feasible ReLU segments. Finally, we
demonstrate the efficiency of the proposed algorithms using numerical
simulations with increasing complexity of the neural network controller
Transferable neural networks for enhanced sampling of protein dynamics
Variational auto-encoder frameworks have demonstrated success in reducing
complex nonlinear dynamics in molecular simulation to a single non-linear
embedding. In this work, we illustrate how this non-linear latent embedding can
be used as a collective variable for enhanced sampling, and present a simple
modification that allows us to rapidly perform sampling in multiple related
systems. We first demonstrate our method is able to describe the effects of
force field changes in capped alanine dipeptide after learning a model using
AMBER99. We further provide a simple extension to variational dynamics encoders
that allows the model to be trained in a more efficient manner on larger
systems by encoding the outputs of a linear transformation using time-structure
based independent component analysis (tICA). Using this technique, we show how
such a model trained for one protein, the WW domain, can efficiently be
transferred to perform enhanced sampling on a related mutant protein, the GTT
mutation. This method shows promise for its ability to rapidly sample related
systems using a single transferable collective variable and is generally
applicable to sets of related simulations, enabling us to probe the effects of
variation in increasingly large systems of biophysical interest.Comment: 20 pages, 10 figure
Neural-Attention-Based Deep Learning Architectures for Modeling Traffic Dynamics on Lane Graphs
Deep neural networks can be powerful tools, but require careful
application-specific design to ensure that the most informative relationships
in the data are learnable. In this paper, we apply deep neural networks to the
nonlinear spatiotemporal physics problem of vehicle traffic dynamics. We
consider problems of estimating macroscopic quantities (e.g., the queue at an
intersection) at a lane level. First-principles modeling at the lane scale has
been a challenge due to complexities in modeling social behaviors like lane
changes, and those behaviors' resultant macro-scale effects. Following domain
knowledge that upstream/downstream lanes and neighboring lanes affect each
others' traffic flows in distinct ways, we apply a form of neural attention
that allows the neural network layers to aggregate information from different
lanes in different manners. Using a microscopic traffic simulator as a testbed,
we obtain results showing that an attentional neural network model can use
information from nearby lanes to improve predictions, and, that explicitly
encoding the lane-to-lane relationship types significantly improves
performance. We also demonstrate the transfer of our learned neural network to
a more complex road network, discuss how its performance degradation may be
attributable to new traffic behaviors induced by increased topological
complexity, and motivate learning dynamics models from many road network
topologies.Comment: To appear at 2019 IEEE Conference on Intelligent Transportation
System
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