In the near future, I expect to work on the following aspects and components of the library:

• Ensuring that the agents module works fully - especially the part that concerns neural networks, evolutionary algorithms, and machine learning. There is a lot of work to be done to improve the efficiency of training using evolutionary algorithms (which cannot be replaced due to the specifics of the tasks for gradient descent methods). The problem is also that the training data is very noisy (which is inevitable since the training data are realizations of stochastic processes), which sometimes makes training models difficult, and sometimes impossible. Work needs to be done to ensure that the partially random nature of the training data does not interfere with training or at least clearly determine to what extent it interferes. Generally speaking, there is a huge field for experimentation in the agents module, designing more and more complex environments and games and correspondingly more complex agents, in order to achieve situations and behaviors that are closest to those that really occur in economics and biology. In particular, agents can be trained on a wide range of types of stochastic processes with the ability to choose between different processes during decision-making, and input data can be not only process parameters but also time series generated by simulations of these processes. The list of applied neural network architectures can also be greatly expanded. For evolutionary algorithms, I am considering integration with the evotorch library in the future. In any case, training evolutionary algorithms is quite computationally expensive, and optimization needs to be addressed.

• Speed optimization, integration with C and Wolfram language to increase computation speed. Sometimes process simulations take quite a long time, and I plan to provide the ability to run simulations in a low-level language (most likely C) directly through the Python interface of the library. Integration with Wolfram Mathematica would, in turn, help with the optimization of symbolic computations where sympy might not cope. The submodule dedicated to symbolic computations constitutes a considerable and quite important part of the library, and I would like to ensure its most efficient operation.

• Integration with domain libraries, primarily in economics, finance, and biology. To make applied work using the Ergodicity Library as efficient as possible, I plan full co-integration of the library with the main libraries in specific sciences. In particular, this involves exporting and importing data, creating custom classes and methods that allow working directly in the domain area without additional programming efforts.

• Deeper implementation of multi-core computations and parallelism. Already at the moment, the library actively relies on multi-core processing - after all, many tasks related to modeling stochastic processes can be solved in parallel. Nevertheless, there are ideas on how to achieve more in this direction and ensure automatic parallelism wherever possible.

• Implementation of additional functionality based on articles and research on ergodicity economics not included in the book Peters, Adamou (2018). Ergodicity Economics. London Mathematical Laboratory. https://ergodicityeconomics.com/publications/. As the field develops, I will try to add tools gleaned from new most interesting and important research.

• Bringing to a full-fledged state some classes and methods that do not yet work as expected - for example, methods for generating processes based on given characteristic functions or some methods related to solving stochastic partial differential equations.

• Various minor work on implementing secondary methods and developing additional functionality.

• Exploring the possibility of applying mathematical apparatus beyond Ito Calculus for stochastic and ergodic analysis.

• Implementation of the library's graphical interface, which will allow easy use of the library by anyone.

• Additional functionality for fat-tailed processes, including for example knew ways to simulated correlated processes, more tools to analyze them and apply symbolic computations, more tools to find patterns in their behavior (including the ensembles of such processes). 

• And of course, implementing feedback and wishes from library users and testers!

 

Any help in these and other directions is welcome. I would especially appreciate the following help:

• Integration with libraries in domain areas and adding domain functionality in general. Here, of course, help from domain experts who know what they need and why in their field would be invaluable.

• Implementation of additional mathematical functionality (both symbolic and numerical solutions) using the most modern and advanced mathematical tools of stochastic analysis and ergodic theory.

• Testing the library.

• Work on the graphical interface.