Computational methods for Cahn-Hilliard variational inequalities

We consider the non-standard fourth order parabolic Cahn-Hilliard variational inequality with constant as well as non-constant diffusional mobility. We propose a primal-dual active set method as solution technique for the discrete variational inequality given by a (semi-)implicit Euler discretization in time and linear finite elements in space. We show local convergence of the method by reinterpretation as a semi-smooth Newton method. The discrete saddle point system arising in each iteration step is handled by either a Gauss-Seidel type method, the application of a multi-frontal direct solver or a preconditioned conjugate gradient method applied to the Schur complement. Finally we show the efficiency of the method and the preconditioning with several numerical simulations

Allen-Cahn and Cahn-Hilliard variational inequalities solved with Optimization Techniques

Parabolic variational inequalities of Allen-Cahn and Cahn- Hilliard type are solved using methods involving constrained optimization. Time discrete variants are formulated with the help of Lagrange multipliers for local and non-local equality and inequality constraints. Fully discrete problems resulting from finite element discretizations in space are solved with the help of a primal-dual active set approach. We show several numerical computations also involving systems of parabolic variational inequalities

Learning Behavior-Grounded Event Segmentations

The event segmentation theory (EST) postulates that humanssystematically segment the continuous sensorimotor informa-tion flow into events and event boundaries. The basis for theobserved segmentation tendencies, however, remains largelyunknown. We introduce a computational model that groundsEST in the interaction abilities of a system. The model learnsevents and event boundaries based on actively gathered senso-rimotor signals. It segments the signals based on principles ofprobabilistic predictive coding and surprise. The implementedmodel essentially simulates, anticipates, and learns event pro-gressions and event transitions online while interacting withthe environment by means of dynamic, predictive Bayesianmodels. Besides the model’s event segmentation capabilities,we show that the learned encodings can be used for higher-order planning. Moreover, the encodings systematically con-ceptualize environmental interactions and they help to identifythe factors that are critical for ensuring interaction success

Embodied learning of a generative neural model for biological motion perception and inference

Although an action observation network and mirror neurons for understanding the actions and intentions of others have been under deep, interdisciplinary consideration over recent years, it remains largely unknown how the brain manages to map visually perceived biological motion of others onto its own motor system. This paper shows how such a mapping may be established, even if the biologically motion is visually perceived from a new vantage point. We introduce a learning artificial neural network model and evaluate it on full body motion tracking recordings. The model implements an embodied, predictive inference approach. It first learns to correlate and segment multimodal sensory streams of own bodily motion. In doing so, it becomes able to anticipate motion progression, to complete missing modal information, and to self-generate learned motion sequences. When biological motion of another person is observed, this self-knowledge is utilized to recognize similar motion patterns and predict their progress. Due to the relative encodings, the model shows strong robustness in recognition despite observing rather large varieties of body morphology and posture dynamics. By additionally equipping the model with the capability to rotate its visual frame of reference, it is able to deduce the visual perspective onto the observed person, establishing full consistency to the embodied self-motion encodings by means of active inference. In further support of its neuro-cognitive plausibility, we also model typical bistable perceptions when crucial depth information is missing. In sum, the introduced neural model proposes a solution to the problem of how the human brain may establish correspondence between observed bodily motion and its own motor system, thus offering a mechanism that supports the development of mirror neurons

Adaptive learning in a compartmental model of visual cortex—how feedback enables stable category learning and refinement

The categorization of real world objects is often reflected in the similarity of their visual appearances. Such categories of objects do not necessarily form disjunct sets of objects, neither semantically nor visually. The relationship between categories can often be described in terms of a hierarchical structure. For instance, tigers and leopards build two separate mammalian categories, but both belong to the category of felines. In other words, tigers and leopards are subcategories of the category Felidae. In the last decades, the unsupervised learning of categories of visual input stimuli has been addressed by numerous approaches in machine learning as well as in the computational neurosciences. However, the question of what kind of mechanisms might be involved in the process of subcategory learning, or category refinement, remains a topic of active investigation. We propose a recurrent computational network architecture for the unsupervised learning of categorial and subcategorial visual input representations. During learning, the connection strengths of bottom-up weights from input to higher-level category representations are adapted according to the input activity distribution. In a similar manner, top-down weights learn to encode the characteristics of a specific stimulus category. Feedforward and feedback learning in combination realize an associative memory mechanism, enabling the selective top-down propagation of a category's feedback weight distribution. We suggest that the difference between the expected input encoded in the projective field of a category node and the current input pattern controls the amplification of feedforward-driven representations. Large enough differences trigger the recruitment of new representational resources and the establishment of (sub-) category representations. We demonstrate the temporal evolution of such learning and show how the approach successully establishes category and subcategory representations

Is it Living? Insights from Modeling Event-Oriented, Self-Motivated, Acting,Learning and Conversing Game Agents

A cognitive architecture is presented, which combines insights from artificial intelligence with cognitive psychology,biology, and linguistics. Using a Super Mario clone, we equipped the simulated agents with (i) motivational behavioral systems,(ii) reasoning and planning capabilities, (iii) event-based schema learning and sensorimotor exploration, and (iv) speech com-prehension and generation mechanisms. The motivational system activates goal events to maintain internal homeostasis. Toinvoke selected events, hierarchical action planning and control unfolds both on an event-schematic and a sensorimotor level.Schema learning is based on the detection of event changes, which are not predicted by the basic sensorimotor forward model.Language is comprehended and generated using context-free grammars linked to the schema-based knowledge structure. Thework offers an approach to develop and thus to ground conceptual, semantic world knowledge in sensorimotor interactions andto couple this knowledge with a language to generate and comprehend language about the agent’s virtual world meaningfully