4,646 research outputs found
A Survey on Continuous Time Computations
We provide an overview of theories of continuous time computation. These
theories allow us to understand both the hardness of questions related to
continuous time dynamical systems and the computational power of continuous
time analog models. We survey the existing models, summarizing results, and
point to relevant references in the literature
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Automatic Generation of Cognitive Theories using Genetic Programming
Cognitive neuroscience is the branch of neuroscience that studies the neural mechanisms underpinning cognition and develops theories explaining them. Within cognitive neuroscience, computational neuroscience focuses on modeling behavior, using theories expressed as computer programs. Up to now, computational theories have been formulated by neuroscientists. In this paper, we present a new approach to theory development in neuroscience: the automatic generation and testing of cognitive theories using genetic programming. Our approach evolves from experimental data cognitive theories that explain âthe mental programâ that subjects use to solve a specific task. As an example, we have focused on a typical neuroscience experiment, the delayed-match-to-sample (DMTS) task. The main goal of our approach is to develop a tool that neuroscientists can use to develop better cognitive theories
Nonlinear model order reduction for problems with microstructure using mesh informed neural networks
Many applications in computational physics involve approximating problems
with microstructure, characterized by multiple spatial scales in their data.
However, these numerical solutions are often computationally expensive due to
the need to capture fine details at small scales. As a result, simulating such
phenomena becomes unaffordable for many-query applications, such as
parametrized systems with multiple scale-dependent features. Traditional
projection-based reduced order models (ROMs) fail to resolve these issues, even
for second-order elliptic PDEs commonly found in engineering applications. To
address this, we propose an alternative nonintrusive strategy to build a ROM,
that combines classical proper orthogonal decomposition (POD) with a suitable
neural network (NN) model to account for the small scales. Specifically, we
employ sparse mesh-informed neural networks (MINNs), which handle both spatial
dependencies in the solutions and model parameters simultaneously. We evaluate
the performance of this strategy on benchmark problems and then apply it to
approximate a real-life problem involving the impact of microcirculation in
transport phenomena through the tissue microenvironment
Grammar Variational Autoencoder
Deep generative models have been wildly successful at learning coherent
latent representations for continuous data such as video and audio. However,
generative modeling of discrete data such as arithmetic expressions and
molecular structures still poses significant challenges. Crucially,
state-of-the-art methods often produce outputs that are not valid. We make the
key observation that frequently, discrete data can be represented as a parse
tree from a context-free grammar. We propose a variational autoencoder which
encodes and decodes directly to and from these parse trees, ensuring the
generated outputs are always valid. Surprisingly, we show that not only does
our model more often generate valid outputs, it also learns a more coherent
latent space in which nearby points decode to similar discrete outputs. We
demonstrate the effectiveness of our learned models by showing their improved
performance in Bayesian optimization for symbolic regression and molecular
synthesis
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