List of questions

Neural Networks applied to the nearly singular systems

Applicability of neural networks (NN)to mechanics systems with light damping, for example, frequently large structural- acoustics Finite Element models have to be reduced in size. The question relates to the applicability of NN for these models in the presence of lightly damped resonances. Typically the response (velocities, forces, mechanical stress, etc) of such a system is sought in frequency domain and a response may exhibit many resonance peaks in the frequency range of interest.

Propagation of model uncertainties originating from PDE with uncertain terms

Frequently there are many alternatives for a term describing a particular physics mechanism in a PDE. The question relates to if there are structured approaches for evaluating the effect of such an function uncertainty. A typical example is the characterization of damping in mechanical systems.

Maintenance Optimization for Fleets

The questions are whether or not there is any going on research on subject of maintenance optimization, especially on opportunity based maintenance or selective maintenance. For references, see attached articles In case there is, it would be really interesting to know which models are considered.

Ant Colony optimization for discrete optimization problems

A general question about the Ant Colony method. Is there any experience working with this algorithm. If so, which applications were considered

General optimization of Electrical Enclosures

This is an interesting multi-physics case where Maxwell equations are strongly coupled with the Navier-Stokes equations and minimizing the losses and the cost as well as cooling efficiently are the objective function of the solution.

Reinforcement Learning for Robot Control

My interest right now is “Reinforcement Learning for Robot Control”. By robot we mean 6/7 DOF arm. The question is can a robot learn a control law when the model of the robot-world interaction is unknown? Not only is it unknown, it is expected to be highly nonlinear and also discontinuous. Controlling a robot to move in free space is easy. It can be done with simple PID controller or even more advanced MPC controller. But controlling a robot in contact-rich environment is very challenging. Reinforcement learning is one way forward but not all questions are answered. How to formulate a reinforcement learning problem? It’s reward function? Policy representation? How to address stability and verifiability? How much physics and optimal control theory can be exploited and how much should be left for learning? Learn end to end visiomotor policy? These are few research questions. This is a hot research area but at this point I am not able to extract a specific topic.

Note: Reinforcement learning can be used for any control problem not just robots.

Reinforcement learning for planning problems

My research interest is reinforcement learning for planning problems, i.e. all control signals are discrete.

· One set of application areas is the policy generation for subsystems working together in parallel, with full information of all states – or with no/little information of other subsystems’ states. (this could be used for robot cell programming and programming of autonomous robots respectively).



· Another application is learning of search heuristic for scheduling/routing problems. By training on a set of cases from a family of problems, learn the heuristics to quickly solve other problems in the family to near-optimality.



· A third application would be to use machine learning to learn search heuristics for robot path planning. In such a case the search space to navigate through is continuous, but your constraints are cluttered in 3D-space. What you want to learn is then a policy where to explore, depending on obstacles, positions of other robots etc.



Also – everything that combines discrete constraint satisfaction problems with continuous variables, I’m always very interested.

Smooth Particle Hydrodynamics (SPH)

Smooth Particle Hydrodynamics (SPH) method is a particle based method which was originally developed for the astrophysicists. But, it becomes very popular to the other research fields for example CFD. SPH is fast and being used to produce very nice and gorgeous fluid flows in video games and movies with very high quality 3D graphics.

· The most common problem with SPH is to satisfy the complex solid boundary conditions properly. The SPH formulation becomes invalid close to the boundary as the distribution function or, kernel gets truncated by the boundary. Satisfying the wall boundary condition is very challenging in SPH algorithm. There are many different ways to treat the wall boundary condition. However, these techniques are very sensitive to high speed and particularly to sharp change in the flow field. The main challenge is to take care of no penetration and no slip condition at the wall.

· Another problem is to implement the inlet/outlet boundary condition, because then it is very difficult to conserve the mass.

· For heat transfer problems, it is important to calculate the temperature gradient in the boundary layer close to the wall which is often very thin. To resolve the thin boundary layer, it requires very small particles which is another limitation for SPH when simulating large domain. Solution for this problem is to work with variable sized particle in different locations of the domain which is very difficult and expensive to maintain in the simulation. Hence, SPH becomes slow.

· How to overcome the problems mentioned above in a mathematically correct way and perform CFD simulations to solve large problems using SPH?

How can the fast multipole method be paralleized for DMP architechture

At Efield we develop and sell a multilevel fast multipole solver for electromagnetic applications. The solver is currently parallelized for shared memory using OpenMP. Since some of the applications (ADAS for cars, RCS, etc) requires very large scale simulations a DMP version of the solver would decrease simulation time and extend the applications we can handle.

Genetic Fuzzy Logic based Artificial Intelligence for Optimization of Telecommunication Networks

When operating a telecommunication network, there are a lot of parameters to tune and a lot of metrics which are affected by those parameters. To find the right parameter setting, which gives optimal performance as indicated by those metrics, is a non-trivial task. Furthermore, different networks in general require different parameter settings.
However, experience show that even though the entire parameter set is large, it is often only a small subset of parameters which have significant influence on performance.
Our question concerns if and how genetic fuzzy logic based artificial intelligence can be used in order to simplify optimization of telecommunication networks, in a similar manner as in the ALPHA project [1] where it is used to control unmanned aircrafts.
References
Ernest et. al., Genetic Fuzzy based Artificial Intelligence for Unmanned Combat Aerial Vehicle Control in Simulated Air Combat Missions, J Def Manag 2016, 6:1.

Partitioning of Directed Acyclic Graphs

Many computer programs can be described as a directed acyclic graphs, where the vertices are functions or subroutines and the edges describe in which order the functions shall be called. Executing such a function graph as is on a multi-core or many-core system is likely to cause congestion in the scheduler, resulting in high over-head and low efficiency. Therefore, the function graph need to be partitioned into a task graph, where each task consists of a sufficiently large number of function calls in order to keep scheduling over-head low. Furthermore, the task graph must also be a directed acyclic graph, just as the function graph, in order to avoid dead-locks. And in a real-time setting, it is also important to minimize the critical path through the task graph.
Today, the partitioning of function graphs into task graphs is done manually, at least at Ericsson. It would be beneficial to automate this process, to relieve software developers from that burden.
Partitioning of large undirected graphs has been thoroughly researched for decades, e.g. for load balancing of parallel PDE solvers, but we are not yet aware of any research about partitioning of directed acyclic graphs, in particular not taking the constraints into account that the resulting graph must also be acyclic and that the critical path through it should be minimized.
We therefore wonder whether there are any known algorithms for this kind of problem or if you have any suggestions how to design a suitable algorithm for it?

American Exercise Boundary in Lattice Models

An important part of the valuation of American options is the provision of information regarding the future conditions under which exercise will be optimal. Extracting this information naturally as a part of lattice model calculations would be very useful, but how to do this efficiently is not entirely clear.

Alternating-Direction Explicit Finite Difference Schemes in Finance

Alternating-direction explicit schemes promise second-order accuracy, unconditional stability and simple implementation. What's the catch, what is the advantage of their implicit counterparts, and how much parallelism do they provide?

Manycore Architectures and Implicit Finite Difference Schemes

High performance computing is consistently developing in the direction of heterogeneous architectures, and particularly the utilization of massively parallel accelerators grows ever more crucial. The systems generated by implicit finite difference schemes are not obviously well-suited for this environment, what can be done to extract more parallelism while retaining the desirable mathematical properties?

Bachelier Model for American Options

One of approaches to price short-term interest rate (STIR) options is based on Bachelier Option Pricing Formula. It is applicable to European-style STIR options. However, for American STIR options one should use numerical methods. It is possible to adapt finite-difference method to solve Bachelier’s partial derivative equation with free boundary, but it is rather time-consuming. Of great interest are accurate analytical approximations for the price of American STIR options based on Bachelier approach.

Feature generation in low signal-to-noise ratio settings

Machine learning methods such as e.g. support vector machines and random forests generally take a number of *features* as input. Features are typically well chosen functions F = F(x_1,x_2,…,x_d) of a potentially large number d of input variables.

The question asked is: how can one construct good features from input variables, for predictions problems in which the SNR is (very) low in the sense that the predictive power of *any* feature is small?

Such settings can be found in e.g. life sciences and financial markets applications.

Preferably, the feature generation process should be as automatic as possible.

Hybrid methods

We are interested in investigating the possibility to couple different numerical approximations for atmospheric simulations. In particular we are interested in high-order stable approximations where the veritical discretization is different from the horizontal discretization. The background to this problem is that we would like to have a very high resolution at the surface of the earth, which gradually reduces to quite coarse resolution outside the planetary boundary layer.