Projects

Here is the list of my recent projects:

Built a pipeline system using LangChain for processing website XML files

Used XML, PyTorch, Python
Data cleaning and pre-processing to optimize input for the LLM.
Integration of HuggingFace's GPT-2 model for intelligent XML generation
Application of prompt engineering techniques for precise and relevant output
Utilization of the HuggingFace Transformers library for model interaction

Augmenting the recurrent states of statistical models using GAN

Used PyTorch, Pandas, Seaborn, Matplotlib
Increased the accuracy of statistical model predictions by 5% by augmenting recurrent states with Generative Adversarial Network (GAN)

Applied ML techniques for detecting dynamic phase transitions

Used Scikit, Python, Seaborn, C++, Matplotlib
Improved accuracy by 3% and efficiency compared to traditional methods

Applied the extreme value statistics (EVS) in strongly correlated networks

Used NetworkX, Python, C++, Matplotlib
Predicting equipment failure: By analysing sensor data from machines and equipment, ML algorithms can identify patterns that might indicate an impending failure. EVS can then be used to estimate the likelihood of a catastrophic failure, allowing for preventative maintenance to be scheduled.
Predicting extreme market crashes: Using historical financial data, ML models can be trained to identify patterns that precede market crashes. EVS can then be used to estimate the probability and severity of future crashes, allowing for better risk management.

Growth processes on network systems

Used Python, C++, NetworkX, Seaborn, Pandas, SciPy, Matplotlib
Developed computational models to analyse growth processes on network systems.
This analysis identified key factors influencing the rate of node addition, such as the presence of highly connected nodes and the availability of resources.
These insights can be applied to optimize the growth and performance of real-world networks in various fields, including social networks, by designing algorithms that incentivize user participation and content creation.

Deep learning-based classification of critical domain walls

Used TensorFlow, Python, Matplotlib, Pandas
Developed a deep learning model for the classification of critical domain walls with an accuracy of 93%. This approach achieved a 3% improvement in efficiency compared to traditional methods, enabling faster and more accurate identification of critical points in spin-glass, Ising and percolation models.

Markovian and non-Markovian random walks

Investigated Markovian and non-Markovian random walks to explore the impact of memory on stochastic processes.
Developed models for fractional Brownian motion and Lévy flights to simulate and analyse these random walk behaviours.
Compared and contrasted the properties of Markovian and non-Markovian processes, including mean squared displacement, first passage time distributions, power spectrum, and maximum entropy.
This research contributed to a deeper understanding of complex systems with memory effects, with potential applications in finance, physics, and biology.

Cellular automaton simulations (GitHub)

Used C++, C#
Developed and implemented cellular automata simulations to explore their mechanics, behaviour and emergence patterns.
This work focused on traffic flow modelling, disease propagation, self-organizing patterns.
The simulations provided valuable insights into critical phenomena, phase transitions, emergence of complex structures.
These findings can be applied to model and understand complex systems in various fields, including biological systems, urban planning, and financial markets.

Applied complex network theory to renewable energies and grid tech

Used C++, Python, Matplotlib, Pandas, Seaborn
Enhanced the analysis and optimization of renewable energy integration and grid technologies by leveraging complex network theory (CNT) and graph neural networks (GNN).
This work focused on modelling power flow in smart grids with high penetration of renewables, analysing the vulnerability of grids to disruptions with increased renewable energy sources.
By applying CNT, the analysis identified critical nodes in the grid for optimal power flow, potential weaknesses in grid infrastructure due to renewable integration.
These insights can be used to develop more resilient and efficient smart grids, strategies for optimal placement and integration of renewable energy sources for a more sustainable and reliable power grid.

Three-dimensional Ising models and Hopfield networks

Explored the interplay between statistical physics and machine learning.
Applied insights from the Ising model to enhance the performance and stability of Hopfield networks, a type of recurrent neural network used for associative memory.
Contributed to the development of more robust and efficient machine learning algorithms, particularly in pattern recognition and memory retrieval.

Multifractality of wave functions at the integer quantum Hall plateau transition

Collaborated with Prof Martin Zirnbauer, a leading physicist in Integer Quantum Hall effects (IQHE).
Modeled and simulated quantum systems while performing detailed statistical analysis.
Utilized the Chalker-Coddington network model to characterize the scaling limit of critical wave function properties.
Discovered a genuine logarithmic scaling toward the renormalization group (RG) fixed point, supported by both theoretical and numerical evidence.
Clarified controversial findings in the field by offering exact results for conductance, current-current correlations, and the multifractal spectrum.

Emergent Pheromone-Guided Strategies: A Statistical and Computational Perspective on Insect Mate-Seeking

Insects navigate their environments by balancing multiple priorities—such as foraging and mate-seeking—using complex, pheromone-mediated search strategies. Through a computational framework grounded in statistical physics, we reveal how varying task priorities give rise to distinct exploration patterns characterized by anomalous scaling in displacement and non-Gaussian (compressed exponential) distributions of encounters. These emergent behaviors not only shed light on the underlying mechanisms that drive insect movement but also offer a blueprint for optimizing encounter frequencies. By reversing these principles, we demonstrate how pheromone-based traps can be strategically designed to lure and remove target species. This work bridges biology, computational science, and theoretical physics, opening new avenues for understanding and manipulating search processes in both natural and engineered systems.

Extreme Value Statistics (EVS) of Correlated Temporal Networks

In classical extreme value theory, the focus is on uncorrelated random variables. It is shown that there exist universal limit laws for the distribution of the maximum M for the case of IID variables. For those systems, one gets three different universality classes (shown in the above figures). Here p(x) is the parent distribution and f(z) is the PDF of M.

For weakly correlated variables, one can provide a general renormalization group type of argument to study the EVS. This technique does not work for strongly correlated and one has to study case by case different models (one-dimensional Brownian motion, branching Brownian motion, random walks, Levy flights, and 1/f^alpha signals are examples of solvable models). For strongly correlated variables, the issue of universality is wide open.

In this study, I sought some universal laws for EVS of various types of correlated temporal networks.

Percolation transition in the shear-driven granular systems

I investigated the criticality of the jamming transition for the shear-driven systems in two dimensions. Here you can see the force chain configurations related to a snapshot.

Effect of geometrical constraints on Abelian, non-Abelian self-organized critical system

I was interested in studying the competition between Abelian and non-Abelian processes in sandpile models (which may exist on a lattice or network) to determine which one is more dominant regarding self-organized criticality. It appears that this dominance depends on the topology of the systems. I aim to achieve a phenomenological interpretation of my results.

Self-Repelling Bipedal Exploration Process

I studied the systems of self-repelling two-leg (biped) spider walk where the local stochastic movements are governed by two independent control parameters, so that the former controls the distance between the legs positions, and the latter controls the statistics of self-crossing of the traversed paths; this backs to the fact that the traces that traversed by the legs of the spider matter, i.e. the traces are self-repulsive in the sense that in each time step t, the random walkers drop a unit of debris at the point that they stand on.

Two-dimensional super-roughening in the three-dimensional Ising model

A random-interface representation of the 3D Ising model, based on thermal fluctuations of a uniquely defined geometric spin cluster in the 3D model (a) and its 2D cross-section (b), is illustrated.

A geometric spin cluster is defined as a set of connected nearest-neighbor sites with like-sign spins, identified by a clustering algorithm. I demonstrated that the global interfacial width varies with temperature across different lattice sizes, revealing critical behavior at Tc where a size-independent cusp forms in 3D, alongside emergent super-roughening observed in its 2D cross-section. I observed that the super-rough state exhibits intrinsic anomalous scaling behavior in local properties, characterized by a set of geometric exponents identical to those found in a pure 2D Ising model.

Universality of Non-Equilibrium Growth Models at Crossing Points

Left: I investigated the universality of height fluctuations at the intersection of two interacting interfaces undergoing non-equilibrium growth processes.

Right: Snapshots depicting the time evolution of height profiles in a flat-wedge geometry."

Each substrate is expected to follow Tracy-Widom distributions. Under specific conditions where both geometries carry equal weight, the behavior is characterized by emerging Gaussian statistics within the universality class of Brownian motion. We propose a phenomenological theory to interpret our results and explore potential applications in non-equilibrium transport and traffic flow.

Classification of boundary curves using Schramm-Loewner evolution (SLE)

The positive-height clusters are depicted in various colors, accompanied by solid lines representing the corresponding spanning iso-height lines. We demonstrate that these curves can be classified using Stochastic Loewner Evolution (SLE).

Sandpile on uncorrelated site-diluted percolation lattice; from three to two dimensions

The BTW sandpile model is studied on a three-dimensional percolation lattice, where the lattice is tuned by the occupation parameter p. In addition to studying three-dimensional avalanches, we investigate avalanches occurring in two-dimensional cross-sections.

Avalanches of three-dimensional small-world networks and their boundary and bulk cross-sections

In many scenarios, understanding the propagation of energy in specific regions of a three-dimensional system with sparsely distributed long-range connections is crucial. In this project, we employ a sandpile model on a three-dimensional small-world network featuring realistic dissipative boundaries and investigate the propagation of energy both in three dimensions and in two-dimensional cross-sections. Two types of cross-sections are defined: one within the bulk of the system and another at the system boundary. The objective is to elucidate how the statistical properties of avalanches in the bulk cross-section converge towards those of dissipative avalanches defined at the boundaries as the concentration of long-range links (α) increases. Numerical analysis demonstrates this convergence follows a power law.

Random walks on intersecting geometries

We present an analytical approach to study simple symmetric random walks on a crossing geometry. The geometry consists of a plane square lattice intersected by nl lines, all converging at a single point (the origin) on the plane.

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