5 research outputs found
Error estimates of residual minimization using neural networks for linear PDEs
We propose an abstract framework for analyzing the convergence of
least-squares methods based on residual minimization when feasible solutions
are neural networks. With the norm relations and compactness arguments, we
derive error estimates for both continuous and discrete formulations of
residual minimization in strong and weak forms. The formulations cover recently
developed physics-informed neural networks based on strong and variational
formulations
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A machine learning approach for smart computer security audit
This thesis presents a novel application of machine learning technology to automate network security audit and penetration testing processes in particular. A model-free reinforcement learning approach is presented. It is characterized by the absence of the environmental model. The model is derived autonomously by the audit system while acting in the tested computer network. The penetration testing process is specified as a Markov decision process (MDP) without definition of reward and transition functions for every state/action pair. The presented approach includes application of traditional and modified Q-learning algorithms. A traditional Q-learning algorithm learns the action-value function stored in the table, which gives the expected utility of executing a particular action in a particular state of the penetration testing process. The modified Q-learning algorithm differs by incorporation of the state space approximator and representation of the action-value function as a linear combination of features. Two deep architectures of the approximator are presented: autoencoder joint with artificial neural network (ANN) and autoencoder joint with recurrent neural network (RNN). The autoencoder is used to derive the feature set defining audited hosts. ANN is intended to approximate the state space of the audit process based on derived features. RNN is a more advanced version of the approximator and differs by the existence of the additional loop connections from hidden to input layers of the neural network. Such architecture incorporates previously executed actions into new inputs. It gives the opportunity to audit system learn sequences of actions leading to the goal of the audit, which is defined as receiving administrator rights on the host. The model-free reinforcement learning approach based on traditional Q-learning algorithms was also applied to reveal new vulnerabilities, buffer overflow in particular. The penetration testing system showed the ability to discover a string, exploiting potential vulnerability, by learning its formation process on the go.
In order to prove the concept and to test the efficiency of an approach, audit tool was developed. Presented results are intended to demonstrate the adaptivity of the approach, performance of the algorithms and deep machine learning architectures. Different sets of hyperparameters are compared graphically to test the ability of convergence to the optimal action policy. An action policy is a sequence of actions, leading to the audit goal (getting admin rights on the remote host). The testing environment is also presented. It consists of 80+ virtual machines based on a vSphere virtualization platform. This combination of hosts represents a typical corporate network with Users segment, Demilitarized zone (DMZ) and external segment (Internet). The network has typical corporate services available: web server, mail server, file server, SSH, SQL server. During the testing process, the audit system acts as an attacker from the Internet
Multi-resolution methods for high fidelity modeling and control allocation in large-scale dynamical systems
This dissertation introduces novel methods for solving highly challenging model-
ing and control problems, motivated by advanced aerospace systems. Adaptable, ro-
bust and computationally effcient, multi-resolution approximation algorithms based
on Radial Basis Function Network and Global-Local Orthogonal Mapping approaches
are developed to address various problems associated with the design of large scale
dynamical systems. The main feature of the Radial Basis Function Network approach
is the unique direction dependent scaling and rotation of the radial basis function via
a novel Directed Connectivity Graph approach. The learning of shaping and rota-
tion parameters for the Radial Basis Functions led to a broadly useful approximation
approach that leads to global approximations capable of good local approximation
for many moderate dimensioned applications. However, even with these refinements,
many applications with many high frequency local input/output variations and a
high dimensional input space remain a challenge and motivate us to investigate an
entirely new approach. The Global-Local Orthogonal Mapping method is based upon
a novel averaging process that allows construction of a piecewise continuous global
family of local least-squares approximations, while retaining the freedom to vary in
a general way the resolution (e.g., degrees of freedom) of the local approximations.
These approximation methodologies are compatible with a wide variety of disciplines
such as continuous function approximation, dynamic system modeling, nonlinear sig-nal processing and time series prediction. Further, related methods are developed
for the modeling of dynamical systems nominally described by nonlinear differential
equations and to solve for static and dynamic response of Distributed Parameter Sys-
tems in an effcient manner. Finally, a hierarchical control allocation algorithm is
presented to solve the control allocation problem for highly over-actuated systems
that might arise with the development of embedded systems. The control allocation
algorithm makes use of the concept of distribution functions to keep in check the
"curse of dimensionality". The studies in the dissertation focus on demonstrating,
through analysis, simulation, and design, the applicability and feasibility of these ap-
proximation algorithms to a variety of examples. The results from these studies are
of direct utility in addressing the "curse of dimensionality" and frequent redundancy
of neural network approximation