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I am going through Modelica libraries. I was wondering, that there are (or i can't found them) ODE's.
For example in the dynamic pipe model of the standard library.
Generally, the Modelica Standard Library contains many dynamic models - i.e. models that can be described with DAEs or ODEs (look for models using the der() operator).
The reason why you don't see any der() operators in DynamicPipe is that it inherits much of its functionality from several base classes - including Modelica.Fluid.Interfaces.PartialDistributedVolume where you will find the differential equation for mass and energy balances.
Modelica.Blocks.Continuous.FirstOrder is an example of a very simple ODE - a first-order low-pass filter.
You might want to consult the free online Modelica book "Modelica by Example". It shows many examples involving ordinary differential equations.
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I have a lot of constraints(in millions) and want to solve a mixed integer problem. Tried using PuLP and OR-Tools(with SCIP solver), but they failed to solve the problem. I tried using DuaLip for parallel/distributed computing using spark, but it doesn't seem to have good documentation for usage. How should I proceed further?
AFAIK there do not exist continuous LP solvers that do distributed computing. That would require some decomposition scheme. As LPs solve very fast we don't use those techniques anymore. An LP with a few million constraints is not very large these days. Quite often interior-point algorithms do quite well on these large problems (relative to Simplex algorithms). We solve LPs of this size on a completely routine basis on fairly standard hardware.
Your PuLP problem is likely more related to PuLP having problems generating the problem than the solver solving it. (Note that PuLP is not a solver). Python based modeling tools may be slower in generating easy LPs than the solver needs to solve it.
Note: the situation for MIP solvers is very different.
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I have seen straight through estimator (STE) in many Neural Network related papers e.g. this and this. But I cannot understand the concept. I wonder if anyone could explain STE or refer me to a simple resource?
A straight through estimator is a way of estimating gradients for a threshold operation in a neural network. The threshold could be as simple as the following function,
As we can see, the derivative of this threshold function will 0 and during back-propagation, the network will not learn anything since it gets 0 gradients and the weights won't get updated.
The concept of a straight through estimator is that you set the incoming gradients to a threshold function equal to it's outgoing gradients, disregarding the derivative of the threshold function itself. This has been shown to perform well in the results (Figure 2) in this paper you have referenced.
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I want to understand the difference between Discrete and Continuous Solver in MATLAB Simulink.
Could anyone explain me this difference in a simple language with examples.
A state for the discrete solver consists only of values. A state for the continuous solver has values AND state derivatives.
In very plain terms, the continuous solvers are used (required) when you have continuous states, for example when using a continuous integrator or derivative block. Conversely, the discrete solvers are used/recommended when you have only discrete states, e.g. a discrete integrator or derivative block. The Simulink diagnostics will flag any solver compatibility issues.
For more details, have a look at the documentation, in particular this page on choosing a solver.
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I have a scalable quadratic programming problem which has around 50-1000 variables with linear constraints. I am trying to find an effective solver for this. The matlab qp solver can only solve to optimality for 100 variables for my problem. Will cplex be any better? Are there any other tools which I can use.
CPLEX will definitely be better. Everything depends on the environment you are working in. If it's not a problem for you to write a C++ program you can try COIN-OR projects, in particular Couenne http://www.coin-or.org/projects/Couenne.xml for nonlinear MIP's and IPOPT http://www.coin-or.org/projects/Ipopt.xml; for Python lovers they have Coopr, DilPy, GrumPy and other projects. You can also try GAMS https://www.gams.com/, it's great for any optimization problem. It's not a solver, more like modeling system with a large number of built in commercial and open-source solvers. It's free as long as your problem has no more than 50 variables and 50 constraints (as far as I remember).
You can try the Opti Toolbox: http://www.i2c2.aut.ac.nz/Wiki/OPTI/
It has an interface to different solvers which you can use in Matlab. (Precompiled mex files.) It can solve quadratic problems.
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What should I use for stock market prediction and why? comparison if you can please.
Udpated: I wanted to use it for stock market movement (up,down) for 1 day.Also,Thank you for your answer it halped
It's not easy to say you which ML algo will give you best perfomance. Especially if not to see which market you want to predict. I recommend you to implement different algorithms and try to train them, because in my practice changing of layers gave different results. SVM sometime was also flexible enough. Also try to implement and check how your training will work on trained and untrained data in order to have really good results. Also analyze how machine learning will work on more predictable sequences ( aka sin, cos, polinomials, randow walks)
Additional field of investigation can be some technical analisis additions: moving averages, stochastics, candle chart patterns, Fibonacci levels.
And finally in order to get money don't rely only on neural network or SVM but use them in conjunction with some trading strategy. For example you can use some trading strategy which has perfomance 30 % and use ML in order to rise perfomance to 60 %