Browsing by Subject "Neural Networks"
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(2023)This work examines how neural networks can be used to qualitatively analyze systems of differential equations depicting population dynamics. We present a novel numerical method derived from physics informed learning, capable of extracting equilibria and bifurcations from population dynamics models. The potential of the framework is showcased three different example problems, a logistic model with outside inference, the Rosenzweig-MacArthur model and one model from a recent population dynamics paper. The key idea behind the method is having a neural network learn the dynamics of a free parameter ODE system, and then using the derivatives of the neural network to find equilibria and bifurcations. We, a bit clunkily, refer to these networks as physics informed neural networks with free parameters and variable initial conditions. In addition to these examples, we also survey how and where these neural networks could be further utilized in the context of population dynamics. To answer the how, we document our experiences choosing good hyperparameters for these networks, even venturing into previously unexplored territory. For the where, we suggest potentially useful neural network frameworks to answer questions from an external survey concerning contemporary open questions in population dynamics. The research of the work is preceded by a short dive on qualitative population dynamics, where we ponder what are the problems we want to solve and what are the tools we have available for that. Special attention is paid to parameter sensitivity analysis of ordinary differential equation systems through bifurcation theory. We also provide a beginner friendly introduction to deep learning, so that the research can be understood even by someone not previously familiar with the field. The work was written, and all included contents were selected, with the goal of establishing a basis for future research.
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(2024)Planning and decision making are active areas of research in cognitive neuroscience that strive to explain how the brain makes decisions in complex scenarios. Research in this field has traditionally been restricted to simplistic experiments such as two-alternative forced choice situations, and has relatively recently broken into more naturalistic settings with the help of computational modeling and games. Importantly, these computational models aim to be interpretable, meaning that they are crafted in a way that what each parameter means has a clear meaning, perhaps in contrast to massive neural networks. However, the latter may better capture more complex behaviors that the hand-crafted model could miss, so it may be desirable to use a neural network as a guide or ``oracle'' to study and improve the parameters to include in the interpretable model. In this thesis, we present GPT-4IAR, a transformer neural network architecture for modeling and predicting human behavior in the board game four-in-a-row (4IAR). Building upon previous studies that use fully connected neural networks to improve models around 4IAR, and the excellent capabilities of the GPT architecture in tasks where data is sequential, we train a transformer on millions of games of 4IAR to study biases that arise in human decision making. Experiments show that conditioning action predictions on longer histories of previous moves leads to improved accuracy over prior state-of-the-art models, hinting at longer-term strategic biases in human gameplay. Reaction time prediction is also explored, showing promise in capturing meaningful gameplay statistics beyond raw actions.
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