Physics-Informed Neural Networks: an AI Approach to Solve Direct and Inverse PDE Problems

Partial differential equations (PDEs) arise naturally when modeling physical phenomena mathematically. The importance of PDE goes far beyond just solving a math problem; they are crucial for many physics and engineering problems; saying that the world is governed by PDEs is not an exaggeration. However, solving a PDE is not always straight- forward; despite their extreme importance, not all PDEs are solvable. Many numerical methods have been devised to solve PDEs over the years, like Finite Element Method, Finite Volume, etc.; nevertheless, these methods can suffer from numerical instability and being computationally expensive. Physics-Informed Neural Networks (PINNs) are a novel approach that uses the properties of deep learning to solve PDEs by combining AI and physics hand in hand without relying on traditional numerical discretization methods. In this thesis, we investigate the capabilities and limitations of PINNs in solving both di- rect and inverse PDE problems. We introduce a novel architecture that can be adjusted to any PDE with any boundary/initial conditions. We also attempt to solve the Firn PDE, a very important and complex PDE. Our findings provide practical guidelines on the imple-mentation of PINNs across different PDEs, highlighting where PINNs succeed and may potentially fail. These findings suggest that PINNs have the future potential to be the go-to PDE solving method

Next-Generation Point-of-Care Cancer Detection: Bioelectronic Mapping of the Malignancy Spectrum

Circulating tumor cells (CTCs) detach from primary tumors, enter the bloodstream, and contribute to disease progression through “metastasis”—the leading cause of cancer-related deaths. CTCs carry vital information about cancer progression; however, their capture and detection remain a major challenge for point-of-care (POC) cancer diagnostics, therapeutic monitoring, and prognostic assessment. This primarily arises from the lack of universal markers capable of isolating CTCs from blood and identifying their metastatic potential. In this work, we aim to advance next-generation POC cancer detection by developing a bioelectronic platform for mapping CTCs across their metastatic spectrum and establishing a novel core technology for their isolation and detection. To achieve this, we utilized in-vitro model of metastasis progression derived from the same cell lineage by varying the expression of Connexin 43 in MDA-MB-231 triple-negative breast cancer cells. In our work, via in-house developed single-cell force microscopy assay, we demonstrated that malignancy correlates with cellular biophysical properties. Highly malignant cells exhibited increased elasticity, cellular softening, and reduced adhesion forces up to ~150 nN, in contrary to cells with lower metastatic potential that showed cellular stiffening, viscous membrane character, and enhanced adhesion of ~350 nN, an almost 60% increase in adhesion strength. Notably, these differences were observed only when cells were in clusters, and the effect disappeared at single-cell state. A first of its kind measurement. Furthermore, we investigated real-time biomechanical responses to Docetaxel (DTX), a microtubule-targeting chemotherapeutic agent, across different metastatic states using Quartz Crystal Microbalance with Dissipation Monitoring (QCM-D). Treatment with 20 nM DTX increased cellular stiffness, with distinct response magnitudes and kinetics between the metastatic cell variants, which correlated with cell aggressiveness and malignancy levels. Additionally, we designed and fabricated a Dielectrophoretic Impedance Spectroscopy (DEPIS) array, with low-impedance and high-sensitivity using additive-manufacturing technology. This array was optimized through finite element analysis simulations to maximize efficiency for CTC capture and characterization in solution. Our results revealed an interplay between cancer cell biophysical and dielectric properties, which correlate with their metastatic states. Highly metastatic cells displayed membrane capacitances of 16.88 ± 3.24 mF m−2, higher than those of less metastatic subtypes with membrane capacitances below 14.3 ± 2.54 mF m−2. These capacitance variations corresponded to distinct crossover frequencies—an essential metric for cell sorting. Additionally, impedance measurements at 1 kHz revealed significant differences in double-layer capacitance among the metastatic subgroups, highlighting DEPIS as a non-invasive and rapid tool for CTC sorting, capture, and classification. Finally, we designed and developed a novel all-planar, high-performance organic electrochemical transistor (OECT) with high reproducibility, amplification (3.8 mS) and rapid response times (0.08 ms). Our OECT-based cancer biosensor revealed that cancer cells with different metastatic states modulate the drain current (IDS) differently. Cells with lower metastatic potential caused a greater attenuation of IDS up to 35% compared to 12% modulation with cells in the higher metastatic spectrum, correlating with their higher adhesion strength and lower membrane capacitance, as established in our previous studies. This work will pave the way for a next-generation POC platform for cancer detection. The unique cellular fingerprints identified can serve as biophysical and bioelectronic biomarkers for distinguishing and sorting CTCs. Our approach holds great promise for liquid biopsy-based cancer diagnostics and monitoring, offering a powerful tool for precision medicine applications

Ultrasound-Based Neuromodulation for Cognition Enhancement: Exploring Frequency-Specific Effects on Hippocampal Neurogenesis in Rats

Neurogenesis, the process of generating functional neurons from neural stem or progenitor cells, holds significant therapeutic potential for treating neurological disorders, including neurodegenerative diseases and cognitive impairments. Neurostimulation, which involves externally modulating neural activity, has emerged as a promising approach to enhancing neurogenesis. While Deep Brain Stimulation (DBS) has shown efficacy in modulating neural circuits and promoting neurogenesis, its invasive nature poses risks such as infection and bleeding, limiting its broader application. In contrast, ultrasound-based neurostimulation offers a non-invasive alternative with substantial potential. Low-intensity ultrasound has been shown to modulate neural activity, enhance synaptic plasticity, and potentially stimulate neurogenesis. This study aimed to investigate the frequency-specific effects of low-intensity ultrasound on hippocampal neurogenesis and its functional outcomes in Sprague-Dawley rats. A four-week experimental protocol was implemented, during which ultrasound stimulation was applied directly to the hippocampus. Three distinct ultrasound frequencies—500 kHz, 1 MHz, and 5 MHz—were systematically examined to determine optimal conditions for promoting neurogenesis. Neural proliferation was assessed using immunofluorescence, with BrdU (5-bromo-2'-deoxyuridine) labeling proliferating cells and NeuN (Neuronal Nuclei) marking mature neurons. Additionally, the novel object recognition (NOR) test, a hippocampal-dependent cognitive task, was used to evaluate functional outcomes, with behavioral metrics including time spent exploring the novel object and latency to explore recorded post-stimulation. The results demonstrated frequency-dependent effects of ultrasound stimulation on hippocampal neurogenesis at both molecular and behavioral levels. Immunofluorescence analysis revealed a significant increase in BrdU-positive cells at 500 kHz, indicating enhanced neural proliferation at this frequency, whereas higher frequencies (1 MHz and 5 MHz) exhibited reduced neurogenic efficacy. Behavioral assessments using the NOR test further corroborated these findings, as rats exposed to 500 kHz ultrasound showed superior cognitive performance, reflected in increased time spent exploring the novel object and shorter latency times. In contrast, rats in the 1 MHz and 5 MHz groups exhibited diminished exploratory behavior and prolonged latency, aligning with the molecular data and suggesting a direct relationship between enhanced neurogenesis and cognitive improvements at 500 kHz

A Minimally-Invasive Method for the Induction of Permanent Myocardial Infarction in Mice: A Novel Approach

Approximately 25% of patients suffering from acute myocardial infarction (MI) develop heart failure, with a survival rate of only 50% beyond five years, primarily due to adverse remodeling of the left ventricle. The mechanisms driving the progression to heart failure remain poorly understood. To address this, preclinical models of MI have been developed globally to better comprehend the disease’s prognosis and to explore potential therapeutic interventions. However, these models rely on the open-chest thoracotomy technique, which exposes the heart for 25 to 30 minutes, increasing the risks of bleeding, infection, larger wound size, pericardial rupture, and aggressive ligation of the left anterior descending (LAD) coronary artery using a 7-0 curved needle, damaging surrounding tissues. Despite various strategies to minimize thoracotomy size, reduce bleeding, and improve outcomes, variability across animal models remains significant. Advances in biomedical technology, enable the induction of MI in a more minimally invasive manner. The aim of this study is to establish a minimally-invasive technique able to induce MI, to validate its efficacy by conducting a comparative analysis against the standard invasive MI model, and to demonstrate that the minimally-invasive technique is able to induce MI with varying sizes. Our study used echocardiography and Doppler imaging, capable of visualizing and precisely locking onto the LAD artery at more than 250 frames per second (fps) for real-time observation in a stable position coupled to an electrocauterization needle that is able to occlude the LAD in seconds (in plane needle guidance to the LAD). Cardiac parameter analysis demonstrated a significant reduction in Ejection Fraction (EF), and echocardiographic assessment of the left ventricle (LV) revealed akinesia of the anterior wall, confirming successful occlusion of the left anterior descending artery (LAD). Additionally, hemodynamic parameters, including left ventricular end-systolic volume (LVESV) and left ventricular end-systolic diameter (LVESD), exhibited marked increase following MI. These findings were consistent with some of results observed in the invasive MI model. Histological analysis further indicated an increase in infarct size and collagen deposition in both the novel and invasive MI models. Notably, the pericardium remained intact in the minimally-invasive technique, whereas it was disrupted in the invasive model. The minimally-invasive model demonstrated its capability to induce varying MI sizes by using pulse wave (PW) Doppler velocity to LAD artery occlusion. Our findings indicate that occlusion of the LAD at regions with higher blood flow results in larger MI, as evidenced by a significant reduction EF, with similar correlations observed for other MI sizes. In conclusion, our minimally-invasive myocardial infarction model offers a superior alternative to the invasive MI model for adoption in research laboratories globally. This approach provides higher translational relevance to clinical settings, demonstrating improved efficiency, reproducibility, and the ability to induce well-controlled MI sizes. Adopting this novel minimally invasive model may therefore enhance the accuracy and applicability of preclinical research, bridging the gap between experimental outcomes and clinical translation

The Reception of Avicenna’s Distinction Between Essence and Existence in the 13th Century Islamic World: The Qūnawī-Ṭūsī Correspondence

The broad focus of this thesis is a correspondence between Sufi mystic Ṣadr al-Dīn al Qūnawī (d.1274) and Persian philosopher and polymath Naṣīr al-Dīn al-Ṭūsī (d.1274). More specifically, this thesis looks at a particular part of this correspondence, the first question (al-masʾala l-ūlā) by al-Qūnawī, and al-Ṭūsī’s reply (jawāb), providing an in depth analysis of the background and context. In this question, al-Qūnawī solicits the Avicennian doctrine of the distinction between essence and existence in everything else other than God and explores how it relates to the Necessary of Being. Upon investigation, this distinction proves to be problematic on a metaphysical level when it comes to God, in light of the identification of God’s essence and existence: how can God, who is utterly unique, simple, and one, be said to exist, at the same time when all other contingent beings are said to exist? Al-Qūnawī’s critique will hinge on this problem of unity vs. multiplicity as he puts forward an ontology of utter oneness of being, the theory of waḥdat al-wujūd. Although he did not coin the term himself, this theory is associated with al-Qūnawī’s master, Ibn al-ʿArabī, and has been used to denote his school of thought. Despite the astute points al-Qūnawī makes, al-Ṭūsī is not convinced and replies to him, bringing forward yet a new ontological understanding of Being, i.e., his concept of al wujūd al-maqūl bi-l-tashkīk, being predicated ambiguously. While al-Ṭūsī thinks of himself as defending a rational philosophical Avicennian paradigm, we will come to appreciate his original contributions to a line of thought that culminates in Mullā Ṣadrā’s thought over 350 years later

Tetherless Tunes: Accelerometer-Enhanced Wearable Device for Recording Songbird Vocalizations

Studies have explored the complex realm of animal communication, utilizing songbirds as a model for vocal learning and social interaction, which have a lot in common with human speaking. Through examining animals such as canaries and zebra finches, scientists have discovered the neuronal foundations of vocal learning, which are similar to aspects of human language acquisition. Important social roles including mate attraction and territorial defense are notably served by songbird vocalizations, highlighting the evolutionary significance of communication systems. This research uses a revolutionary method that records bird songs using a wireless wearable device to go further into these social connections. Accelerometers have several advantages over ordinary microphones, especially when it comes to separating individual bird calls/songs from background noise. The study uses state-of-the-art wearable equipment with a vibration sensor to record sound accurately and connects it to an advanced processing system for amplification and filtering. This novel approach to recording songbird vocalizations promises improved fidelity and clarity, and more freedom of movement for subject songbirds, providing fresh insight into the subtleties of social communication in bird species and others too

Modeling of CO2 Flow with Impurities

Carbon Capture, Utilization, and Storage (CCUS) plays a pivotal role in reducing greenhouse gas emissions, essential for limiting global warming to below 1.5 °C by 2100 and achieving carbon neutrality by 2050. Modeling carbon dioxide (CO₂) density is crucial for optimizing CO₂ transportation and storage systems. However, captured CO₂ streams, often originating from power sources, contain impurities such as Oxygen (O₂), Nitrogen (N₂), Carbon Monoxide (CO), Argon (Ar), Sulfur Dioxide (SO₂), Hydrogen (H₂), Methane (CH₄), Water (H₂O), and Hydrogen Sulfide (H₂S). These impurities significantly impact transmission properties and challenge the predictive capabilities of current equations of state (EoS). To address these challenges, this study utilized a comprehensive dataset comprising 134,204 density data points to evaluate the performance of 14 EoSs, including cubic, virial, physical, and multi-parameter equations. A versatile computational framework was developed, capable of calculating a range of thermodynamic properties beyond density, such as fugacity and its derivatives, enthalpies, and pressure derivatives. Within the development process, various numerical solvers were implemented to enhance computational efficiency, and genetic algorithms were adopted for better predictive performance. This robust framework provides researchers with a powerful tool for advancing CCUS technology, laying the foundation for future studies in thermodynamic modeling and system optimization. For density predictions, the research adopted a dual approach. Machine learning (ML) techniques, including Random Forest, Gradient Boosting, and Neural Networks, were employed to enhance predictive accuracy. These models demonstrated robust performance across complex thermodynamic regions by leveraging a combination of experimental and synthetic data (R² > 0.96). Synthetic data, generated within CCUS pipeline operating conditions using the best-performing EoSs, primarily multi-parameter equations, exhibited an Absolute Average Relative Deviation below 3%. On the other hand, the second approach utilized ranking EoS performance across temperature, pressure, and composition intervals, analyzed using Pareto plots and decision trees with Entropy and Gini indices. This systematic framework identified the optimal applicability ranges for each EoS, shedding light on their strengths and limitations. The integration of ML with interval-based sorting allowed for precise density predictions and reliable assessments of model stability under diverse conditions. The scope of the study extended to stability analysis, evaluating thermodynamic behavior and ensuring reliable predictions critical for the safe and efficient operation of CCUS systems. By assessing phase behavior, stability limits, and operational conditions, the study addressed key challenges in CO₂ pipeline systems and laid the groundwork for their effective design and management. Building on these insights, the research applied the findings to optimize CO₂ transmission networks. A case study was conducted, exploring mass and molar balances, energy balances, system stability, pressure and temperature drops, and viscosity modeling. This comprehensive analysis provided actionable insights into the operational dynamics of CO₂ pipelines, enabling precise predictions and optimizations for real-world applications. To the best of our knowledge, no previous study has utilized such an extensive dataset, evaluated such a diverse array of EoSs, or incorporated this innovative hybrid approach alongside practical case studies and a computational framework of this breadth. These findings provide a robust platform for improving the efficiency, reliability, and scalability of CO₂ transportation and storage systems, further supporting CCUS’s pivotal role in achieving global climate objectives

Predicting Emergency Department Bounce Backs: A Machine Learning Approach

In recent years, there has been a growing interest in utilizing machine learning to predict the likelihood of specific outcomes, particularly in emergency medicine. This thesis focuses on applying machine learning techniques to predict emergency department (ED) bouncebacks—unscheduled patient revisits to the ED within 72 hours—which significantly strain resources, contribute to overcrowding, and often highlight gaps in clinical care in the ED. This study specifically targets high-risk ED revisits that result in hospital admission. Methods: Patient data from a major academic hospital in Lebanon was analyzed using various machine learning algorithms, including logistic regression, neural networks, LightGBM, and XGBoost. Innovative approaches, such as frequency encoding for high-cardinality categorical variables like diagnoses and chief complaints, were employed to optimize model performance while minimizing computational complexity. A temporal training strategy was implemented, training models on data from 2018 to 2022 and part of 2023, with predictions made on the remaining portion of 2023. For the refined model, the dataset was reduced to the top 48 features of importance, supplemented with medication data, to enhance prediction accuracy further. Results: In the initial analysis, XGBoost demonstrated the highest performance among all models, achieving a sensitivity of 0.97, precision of 0.83, and an AUC-ROC of 0.99. Key predictors identified by the model included arrival-to-disposition duration, Age, Diagnosis, BP_Systolic, and Chief Complaint. In the refined model, the XGBoost model trained on a reduced feature set achieved a sensitivity of 0.86, specificity of 0.98, precision of 0.71, and an AUC-ROC of 0.99 on the test set. The refined model confirmed the importance of temporal variables, such as arrival-to-disposition duration and triage duration, alongside patient-specific and clinical features. Although the refined model exhibited a slight decrease in sensitivity, it remained the preferred choice due to its reliance on the most influential features identified in the initial analysis. Furthermore, it was trained using a temporal validation approach that mirrors real-world clinical scenarios, where models are trained on past data and tested on unseen future cases. This strategy enhances the model’s generalizability and practical applicability in dynamic healthcare environments. At the same time, incorporating medication data further improved predictive performance. Conclusion: This research highlights the potential of machine learning to support clinical decision-making by identifying high-risk ED revisits. The findings demonstrate that integrating medication data, leveraging frequency encoding for high-cardinality features, and applying temporal validation strategies enhance model performance and generalizability. By optimizing feature representation and incorporating both historical and recent patient data, the initial and refined models provide a scalable framework for predictive modeling. These approaches contribute to more accurate identification of high-risk ED bounce backs and support the future integration of machine learning in clinical practice

The Effects of Moringa oleifera, Quercetin and Myricetin on Cholesterol Levels in HepG2 Cells in vitro as Well as on Enzymes Regulating Cholesterol Homeostasis in silico

Hypercholesterolemia, a major risk factor for cardiovascular diseases and atherosclerosis, is primarily managed with statins, which inhibit HMG-CoA reductase (HMGCR) and upregulate LDL receptor expression. However, prolonged statin use is associated with adverse effects, necessitating safer alternatives. Moringa oleifera (MO) has garnered attention for its diverse biological activities, including anti-atherosclerotic, anticancer, antidiabetic, antimicrobial, anti-inflammatory, and hypocholesterolemic effects. Given its widespread consumption as a tea beverage, we explored the effects of aqueous MO leaf extract on cholesterol levels and its potential to enhance statin sensitivity, thereby reducing the required dosage and mitigating side effects. To evaluate this, we employed both in vitro and in silico approaches. We assessed the effects of MO extract, simvastatin, and their combination on cell viability, reactive oxygen species (ROS) levels, and cholesterol homeostasis in HepG2 cells. Cells were treated for 24 and 48 hours with MO extract (0.015% and 0.03%) or simvastatin (10 μM). Both treatments led to a dose-dependent but time-independent decrease in cell viability. Consistently, MO extract (0.03%) significantly increased ROS levels, which were restored to baseline with N-acetylcysteine (NAC) pretreatment, whereas simvastatin had no significant ROS impact. The combination treatment partially restored cell viability, but ROS levels remained comparable to MO treatment alone. Cholesterol levels, normalized to protein content, showed the following reductions: a) 20% with simvastatin alone; b) 58% with MO extract alone; c) 70% with the combined treatment These results suggest an additive rather than synergistic effect, likely due to multiple bioactive compounds in MO extract targeting different pathways. Among these, polyphenols such as quercetin and myricetin are abundant in plant extracts. Notably, quercetin and myricetin were non-toxic at most concentrations, except for myricetin, which caused ~30% cell death at 60 μM, in alignment with ROS levels. Preliminary data showed that both flavonoids significantly reduced cholesterol levels within 24 hours, surpassing simvastatin treatment. Computational tools were employed to assess the binding affinities of simvastatin, quercetin, and myricetin with key proteins involved in cholesterol homeostasis. Docking studies revealed: a) Simvastatin competitively binds to the HMGCR active site, extending into the CoA and NADPH binding pockets; b) Quercetin and myricetin primarily occupy the NADPH binding site, suggesting an alternative mechanism of HMGCR modulation. Additionally, binding affinities of these compounds with cholesterol-regulating proteins (HMGCR, SREBP2, LXR, LCAT, ACAT, and CYP8B1) were strong, indicating their potential as cholesterol-modulating agents. ADME and toxicity profiling further supported their pharmacological viability, as both flavonoids complied with Lipinski's rule of five. This study highlights Moringa oleifera and its polyphenolic components as promising, cost-effective adjuncts to statins for cholesterol management. Their ability to enhance statin efficacy while potentially reducing dosage and side effects warrants further investigation into their therapeutic applications in hypercholesterolemia treatment

Antioxidant Properties of Functionalized Tomato Sauce and Leather

As global concern about health, sustainability and food security grow, valorizing food byproducts has become an essential strategy in functional food development. In this context, this study aimed to develop and evaluate functional tomato-based product (tomato leather and tomato sauce) by incorporating tomato byproducts with key mediterranean ingredients such as olive powder, pea protein and aromatic herbs. The tomato byproducts were processed into powdered form and incorporated into new formulations of tomato leather and sauce. In this study, Soxhlet extraction was used to measure total phenolic content (TPC) and antioxidant activity assessments were conducted using the Folin-Ciocalteu (F-C) method and ABTS essay. Accelerated shelf-life analysis (high temperature- high humidity) over 12 weeks evaluated changes in antioxidant potential, color, pH, water activity, and microbial safety of the newly formulated tomato products. Statistical analysis assessed differences and antioxidant potential and product stability. Results showed that tomato seeds had the highest TPC (91.43 mg GAE/100 g), while the skin exhibited better antioxidant potential (31.45 μmol TE/g). The tomato leather, enriched with olive powder and spices, had higher TPC (210.1 mg GAE/100 g) and antioxidant activity (41.02 μmol TE/g) compared to the tomato sauce enriched with olive powder and tomato peel powder (142.79 mg GAE/100 g; 23.85 μmol TE/g). A strong correlation (Pearson's coefficient R = 0.953) between TPC and antioxidant potential was observed. Over 12 weeks, tomato leather maintained stable water activity and microbial load, though its pH decreased. Its antioxidant potential showed an overall increase, linked to color darkening due to Maillard reactions. Tomato sauce showed fluctuations in water activity and a slight decrease in pH, with antioxidant potential increased over time, correlated with color changes. The study demonstrates the potential of using tomato byproducts and Mediterranean ingredients to enhance both sustainability and nutritional value