Ali Namadchian

23 Questions 45 Answers 0 Followers

Questions related from Ali Namadchian

Is it necessary for engineers to know the definitions of mathematical spaces?

We know that mathematicians study different mathematical spaces such as Hilbert space, Banach space, Sobolev space, etc... but as engineers, is it necessary for us to understand the definition of...

10 October 2019 5,075 4 View

Does Fokker-Planck equation give us the exact measure of the statistical ensemble of the trajectories of the stochastic differential equation?

It is known that the FPE gives the time evolution of the probability density function of the stochastic differential equation. I could not see any reference that relates the PDF obtain by the FPE...

10 October 2019 9,935 6 View

Is it possible to stabilize an Infinite-dimensional system by stabilization of the corresponding approximated finite-dimensional system?

we can approximate an infinite-dimensional system with a finite-dimension system, (for example by proper orthogonal decomposition) If we stabilize the approximate finite dimension of an...

10 October 2019 342 6 View

Is there a general framework to compute the reachability set of nonlinear affine-control systems?

for linear control systems x_dot=Ax+Bu the reachability set can be calculated using the Image of the controllability matrix, i.e R=([B AB A^2B,....,]) and reachability set=Im(R) when rank(R)=n,...

01 January 2019 1,960 3 View

In stochastic systems(SDEs), Most of the time we assumed that the disturbance and noise vanish at the equilibrium point, is it reasonable assumption?

One of the main stability theories for stochastic systems is stochastic Lyapanuv stability theory, it is the same as Lyapanuv theory for deterministic systems. the main idea is that for the...

01 January 2019 4,397 4 View

Under which condition it is possible to change the dynamics of a nonlinear system to an arbitrary dynamic with feedback control input?

Imagine we have an ODE system x_dot=[f1(x,u), f2(x,u), f3(x,u),....fn(x,u)] where f1,..,fn are nonlinear functions of control input u and states x, x is member of R^n and u is member of...

01 January 2019 7,543 6 View

Is it possible to prove the stability of a continuous time system from its corresponding discrete version?

In a simplest case imagine we have a continuous finite-dimensional dynamic system described by and ODE x_dot=f(x) (1) , Is it possible to prove the asymptotic stability of (1) by...

12 December 2018 5,381 30 View

Which one is a stronger stability condition? Lyapunov stochastic stability or detailed balance?

in most cases for continuous time stochastic systems which are modeled by SDE, the Lyapunov stability conditions can guarantee the stochastic stability of the system, another definition In...

12 December 2018 4,016 4 View

Is it possible to establish the stability results based on pseudo-spectra for a linear differential operator?

In the theory of the stability of the differential operators, one could prove the stability results based on spectra of an operator, (all eigenvalues must be negative for example). one problem...

11 November 2018 2,954 7 View

Which neural network structure is better for approximation of dynamical systems?

there are different kinds of neural networks. MLP, RBF, LSTM, recurrent, ... I have to approximate a dynamical system with neural network, which type of NN is more suitable for this task?

09 September 2018 2,279 5 View

What is the best method for generating a data-set for training in high dimensional function approximation with neural network?

Imagine we have an 7-D function f(P_i), i=1,...,7. Fortunately, we can create our own data sets for training, i.e we can choose as many samples from the sample space of each P_i (the sample space...

08 August 2018 6,816 5 View

How to approximate high-dimensional function with Neural network?

I need to approximate a 11-D function y=f(xi) i=1,...,11 I know how many points to select in each direction. 30 points for i=1,2,3 and 8 points for i=4,...,11 the input data set will be the tensor...

07 July 2018 7,339 2 View

Is it possible to train neural network with mini-batch in newtons method or Levenberg-Marquardt method?

I have a large data set for training neural network and computationally they can not be fed to NN because of computers lack of memory, So is it possible to train the NN with mini-batch by...

07 July 2018 9,066 2 View

What is the best method for constrained optimization?

what is the best method for constrained optimization ( in terms of the speed of the convergence an accuracy)? I want to train the parameters of the neural network with some constraints on the...

06 June 2018 1,686 17 View

Is Levenberg-Marquardt an appropriate method for training RBF neural networks?

I am using LM algorithm to train RBF neural network, but it seems it does not converg to an optimal solution,(it works quit well for MLP networks). in LM training how we should choose the initial...

06 June 2018 4,418 5 View

MLP or RBF?

which networks outperform the other in function approximation. here is the conditions for comparison: 1- In the RBF network the centers ,weights, biases and scale parameters can be trained. 2-...

06 June 2018 2,874 10 View

In neural network training (back propagation gradient descent training) is the calculated gradient exact value or it is an approximated value?

in back propagation neural network training, using gradient decent, the derivative of weights with respect to error are calculated by back propagation algorithm.is this calculated value the exact...

05 May 2018 8,440 6 View

Which algorithm is the fastest algorithm for training neural network?

I am trying to train a complex system by neural net with Levenberg-Marquardt algorithm, it is faster than stochastic gradient descent, bot it is not fast enough. which training algorithm is the...

05 May 2018 2,355 7 View

Why multi hidden layer NN with few neurons in each layer is a better approximator than a one hidden layer NN with many hidden neurons?

for example for approximation of a 2-D function (2-D Gaussian distribution) a neural net with 2 hidden layer with 3 neurons in each layer is a much better approximator than a one hidden layer...

05 May 2018 2,889 5 View

How to form the probability density function of a variable based on polynomial expansion coefficient?

the gPC is used for uncertainty quantification, I find the gPC coefficients for Z=f(theta),where theta is a random variable(it may have any kind of pdf), I know the first coefficient a0 is the...

01 January 2018 5,549 5 View

Is it possible to determine the type of the pdf of the states of a dynamical system based on pdf of system random variables and the system dynamics?

for example the dynamical system is x_dot=f(x,t,theta), theta is a random variable, which can have Gaussian, Gamma, uniform, multi modal Gaussian or any other probability distribution. is it...

01 January 2018 1,845 3 View

In Generalized Model predictive control Strategy what to do when our linear system has non-zero feedthrough matrix?

In most of the literature for Generalized MPC, it is assumed that D matrix in state space model of the system is zero, I have a system with non-zero D (not a strictly proper system), what should I do?

12 December 2017 1,422 1 View

Is it really possible to predict the stock price by Artificial intelligence and make money out of that?

we know that as mathematician the stock price is a stochastic process than can be modeled by stochastic differential equation and it can not be predicted. but in the view of data scientists and...

01 January 1970 2,930 6 View