This paper presents a novel phase-field modeling approach for fluid dynamics, specifically designed to accommodate and accurately represent non-Newtonian viscosity. Traditional phase-field methods often struggle to capture the complex behavior of fluids exhibiting non-linear viscosity distributions. We introduce a modified diffusion equation incorporating a dynamically adjusted viscosity term, effectively integrating the non-Newtonian characteristics of the fluid into the phase-field framework. This model offers improved accuracy and robustness in simulating various fluid flow scenarios, particularly those involving complex rheological properties. The development of this model provides a significant advancement in the representation of fluid dynamics, offering a more realistic and computationally tractable model for a wide range of applications.
Jincheng Zhang· Zenodo (CERN European Organi...· 0 citations
This paper explores the extension of standard diffusion equations to incorporate a landscape parameter, introducing a feedback loop that drives the evolution of diffusion patterns. Traditional diffusion models, while widely used, often lack the capacity to generate complex and unpredictable behavior. We propose a novel mechanism – a landscape parameter influencing diffusion rate – to mimic this complexity, resulting in emergent patterns and novel dynamics. The paper details the mathematical framework of this approach and provides preliminary results demonstrating the generation of distinct diffusion landscapes. The core claim is that this framework allows for a significantly deeper understanding and control of diffusion processes, opening avenues for applications in materials science, fluid dynamics, and potentially, complex systems modeling.
Jincheng Zhang· Zenodo (CERN European Organi...· 0 citations
This research investigates the emergence of complex patterns within stochastic diffusion processes, proposing a novel approach centered on identifying and quantifying 'emergent complexity' through the application of a "statistical resonance" algorithm. We explore how this algorithm maps information flow across a network of diffusion processes, revealing hidden correlations and structures that contribute to complex dynamics. The core claim is that this method offers a fundamentally different perspective on understanding these systems, potentially leading to enhanced predictive capabilities. The paper details the algorithm's design, its methodology for identifying emergent patterns, and its implications for analyzing and forecasting complex behavior within stochastic diffusion models. We provide a preliminary assessment of the algorithm's efficacy and discuss future research directions focused on expanding the scope of its applicability.
Jincheng Zhang· Zenodo (CERN European Organi...· 0 citations
This paper proposes a novel computational paradigm, termed Algorithmic Morphogenesis, which posits that complex computation can emerge through the controlled diffusion of algorithmic elements within a system. The core idea is that a collection of interconnected agents, each governed by a simple algorithmic rule, can, when coupled with a probabilistic diffusion mechanism, spontaneously generate intricate and potentially useful computational structures. The system operates on the principle of algorithmic "flow" between agents, guided by specific criteria. This approach draws inspiration from biological morphogenesis, specifically the self-organizing processes observed in developing organisms. The key mathematical framework involves stochastic differential equations governing the movement of algorithmic elements and agent interaction rules expressed through Boolean logic. We will demonstrate the potential of this framework to generate complex patterns, suggesting a new avenue for designing systems capable of self-organization and adaptation without explicit, centralized control. The proposed methodology offers a shift from traditional, top-down computational approaches to a bottom-up, emergent perspective. The central equation describing the diffusion process is: *dXi(t) = a(Xi(t)) * dSi(t) + σ(Xi(t)) * dW(t)* Where *Xi(t)* represents the concentration of algorithmic element *i* at time *t*, *a(Xi(t))* is the diffusion coefficient dependent on *Xi(t)*, *Si(t)* is a stochastic increment, *σ(Xi(t))* is the volatility of the stochastic increment, and *W(t)* is a Wiener process. Agent interaction is modeled via a Boolean logic gate network with probability *pij* representing the chance of element *i* diffusing to agent *j*. The system's evolution is determined by a Markov chain, where the state represents the configuration of algorithmic elements across the agents.
Jincheng Zhang· Zenodo (CERN European Organi...· 0 citations
Quantum annealing offers a novel approach to simulating diffusion processes, promising accelerated optimization and enhanced pattern generation. This paper explores the potential of this technique to address a critical bottleneck in simulating diffusion, specifically focusing on the efficient exploration of the solution space. We detail a new algorithm employing quantum annealing to optimize diffusion model parameters, demonstrating a significant speedup compared to classical methods. The core mechanism centers on leveraging quantum annealing's ability to identify optimal solutions through a probabilistic search process. This approach offers a pathway towards more realistic and complex diffusion patterns, with implications for materials science and biology.
Jincheng Zhang· Zenodo (CERN European Organi...· 0 citations
This paper presents a novel theoretical framework for understanding and modeling temporal dynamics, focusing on the propagation of patterns and information across spatial and temporal scales. The core of the work centers on the development of a model incorporating non-linear interactions and diffusion processes, utilizing a diffusion equation that explicitly models the relationship between the diffusion rate and the underlying geometry. We explore a model predicated on the principle of 'complex, non-linear interactions' driving the spread of temporal dynamics. The model's design aims to address the limitations of existing approaches by providing a more nuanced and predictive framework for analyzing and manipulating temporal phenomena. The resulting model offers a potential pathway towards improved understanding and control of complex systems exhibiting temporal dynamics.
Jincheng Zhang· Zenodo (CERN European Organi...· 0 citations
Graph Neural Networks (GNNs) have demonstrated remarkable success in various domains, including social network analysis, drug discovery, and recommendation systems. However, a significant limitation of many existing GNN models lies in their reliance on static attention mechanisms. These mechanisms often assign fixed weights to neighbors, neglecting the dynamic and evolving nature of graph relationships. This paper introduces a novel approach – Contextual Graph Neural Networks with Dynamic Attention Mechanisms – designed to overcome this limitation. The core idea is to develop an attention mechanism that adapts its weights based on the current node's neighborhood, the message content being exchanged, and the overall graph structure. This dynamic adaptation allows the network to capture more nuanced and context-dependent relationships within the graph, leading to improved node representations and enhanced message passing. We formally describe the model, its key components, and the underlying mathematical framework. We argue that this approach represents a significant advancement in GNN research, offering the potential for greater accuracy and robustness in complex graph-structured data.
Jincheng Zhang· Zenodo (CERN European Organi...· 0 citations
Accurate urban traffic flow prediction is crucial for intelligent transportation systems, urban planning, and resource allocation. Traditional traffic forecasting methods often struggle to capture the complex spatiotemporal dependencies inherent in urban traffic networks. This paper proposes a novel approach utilizing multi-scale spatio-temporal graph neural networks (MSST-GNNs) to address this challenge. The core idea is to integrate traffic data at various scales – street, regional, and city levels – and leverage the power of graph neural networks to learn intricate traffic patterns. The MSST-GNNs construct a graph representation of the urban road network, where nodes represent road segments and edges represent connectivity. The model then employs a multi-scale architecture to capture both spatial and temporal dependencies effectively. Specifically, we propose a hierarchical graph convolutional network (HGCN) that progressively aggregates information from finer to coarser scales, incorporating both spatial and temporal context. The HGCN is integrated within a recurrent neural network (RNN) to model temporal dynamics. The resulting MSST-GNNs achieve state-of-the-art performance on several benchmark urban traffic flow datasets. Experimental results demonstrate the effectiveness of the proposed approach in improving prediction accuracy compared to traditional methods and existing graph neural network models. The key contributions of this work are the novel MSST-GNN architecture, the hierarchical graph convolutional network, and the effective integration of multi-scale spatio-temporal data.
Jincheng Zhang· Zenodo (CERN European Organi...· 0 citations
This paper explores the application of Graph Neural Networks (GNNs) for automated drug molecule design. Traditional drug discovery relies heavily on empirical methods and serendipitous findings, often suffering from high costs and low success rates. We propose a novel approach that leverages the inherent structural information within molecules by representing them as graphs and utilizing GNNs to learn the complex relationships between molecular structure and biological activity. The core claim of this work is the ability to automatically design drug molecules using GNNs. The mechanism involves graph representation learning and generation, enabling the model to predict and generate novel molecules with desired properties. This research offers a new paradigm for drug design, potentially accelerating the discovery process and improving the efficiency of identifying promising drug candidates. The key contributions of this work are the demonstrated effectiveness of GNNs in capturing structural features and predicting biological activity, and the framework for automated molecule generation. Further research will focus on incorporating more sophisticated molecular representations and expanding the scope of target diseases. ---
Jincheng Zhang· Zenodo (CERN European Organi...· 0 citations
This paper investigates the application of Graph Neural Networks (GNNs) to the domain of hardware design space exploration. Traditional design exploration methods often struggle to effectively capture and optimize the intricate dependencies inherent in complex hardware architectures. We propose a novel framework utilizing GNNs to represent hardware designs as graphs and learn to predict key design metrics, such as performance and power consumption, directly from the graph structure. The core claim is that GNNs can provide a more efficient and accurate approach to design space exploration compared to conventional methods. We detail the methodology, including graph representation, GNN architecture selection, and training strategies. The results demonstrate the potential of GNNs to uncover promising design alternatives and improve hardware performance and efficiency. This work contributes to a new paradigm in hardware design, leveraging the power of deep learning for automated design optimization.
Jincheng Zhang· Zenodo (CERN European Organi...· 0 citations
Predicting protein function and understanding protein-protein interactions (PPIs) are central challenges in modern biology. Protein-protein interaction networks, representing these interactions, are inherently complex and dynamic. Traditional methods often struggle to capture the temporal evolution of these networks, failing to account for changes in interaction strengths and patterns over time. This paper proposes a novel framework for learning representations of PPI networks that integrates both structural and temporal information. We leverage graph neural networks (GNNs) to encode the network topology and incorporate temporal convolution layers to model the temporal dynamics of interactions. Furthermore, attention mechanisms are utilized to focus on the most relevant interactions within the network context. The resulting learned representations can then be used for various downstream tasks, such as predicting protein function, identifying novel PPIs, and forecasting network changes. Our approach demonstrates a significant improvement in prediction accuracy compared to existing methods, highlighting the importance of temporal dynamics in PPI network analysis.
Jincheng Zhang· Zenodo (CERN European Organi...· 0 citations
This paper presents a novel approach to robot control in complex, multi-agent environments by leveraging relational reinforcement learning (RRL) and graph neural networks (GNNs). The core idea is that robots benefit significantly from understanding and reasoning about the relationships between themselves and their surroundings. Traditional reinforcement learning methods often struggle in scenarios where the reward signal is not directly tied to individual actions but depends on the overall state and interactions within a system. Our proposed framework addresses this limitation by employing a GNN to explicitly model the relationships between robots and environmental elements. This graph representation allows the GNN to capture contextual information and relational dependencies, which are then used by the RRL algorithm to learn optimal policies. We demonstrate the effectiveness of this approach through a theoretical analysis and a conceptual framework, highlighting its potential to improve robot performance in scenarios demanding sophisticated relational reasoning. This work establishes a foundation for future research in combining relational reasoning with deep learning techniques for robust and adaptive robot control.
Jincheng Zhang· Zenodo (CERN European Organi...· 0 citations
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