Description:The present invention relates to the field of computational fluid dynamics, soft matter physics, and artificial intelligence, with particular emphasis on developing a machine learning framework for modeling and predicting mass transport phenomena in non-Newtonian fluids under peristaltic motion. More specifically, the invention resides at the intersection of fluid mechanics, transport processes, and data-driven modeling, where conventional analytical and numerical techniques face limitations in addressing the nonlinear rheology, dynamic boundary conditions, and complex spatiotemporal interactions inherent in peristaltic systems. Non-Newtonian fluids, which are ubiquitous in physiological contexts such as blood, chyme, and mucus transport, as well as in industrial processes including polymer extrusion, food processing, and microfluidic devices, exhibit non-linear viscosity and viscoelastic behavior that challenge classical Newtonian-based models. The field of the invention introduces a novel integration of supervised and physics-informed machine learning algorithms that can capture these complex transport dynamics more accurately and efficiently than traditional computational methods. The invention further encompasses the design of hybrid neural network architectures capable of embedding governing conservation laws, rheological models, and peristaltic wave parameters to ensure physical fidelity in predictive outcomes. By situating itself within applied fluid dynamics and intelligent computation, this invention provides a transformative tool for advancing research and applications in biomedical engineering, pharmaceutical sciences, microfluidics, and process industries, where precise modeling of mass transport under peristaltic motion is critical for optimizing system performance, improving product reliability, and enabling real-time predictive control.

Background of the proposed invention:

Peristaltic motion, a fundamental mechanism of fluid transport characterized by wave-like muscular contractions or imposed boundary deformations, plays a critical role in both natural and engineered systems, ranging from gastrointestinal processes and blood circulation to industrial pumping, food processing, and microfluidic applications. The dynamics of peristaltic transport become increasingly complex when dealing with non-Newtonian fluids, which deviate from classical Newtonian behavior by exhibiting properties such as shear-thinning, shear-thickening, viscoelasticity, and yield stress. Traditional analytical approaches, often relying on simplified assumptions such as low Reynolds number, long wavelength approximations, or linearized rheological models, fail to adequately capture the intricacies of real-world peristaltic transport, particularly in physiological contexts where biological fluids like blood, mucus, and chyme demonstrate highly nonlinear rheology. Likewise, numerical simulations based on computational fluid dynamics (CFD) and finite element or finite difference methods, while powerful, are computationally expensive, highly sensitive to mesh refinement and stability constraints, and often lack the scalability required for real-time applications or parameter sweeps across diverse operating regimes. These challenges are further compounded by the coupled nature of mass transport, where solute dispersion, diffusion, and mixing efficiency are directly influenced by spatiotemporal velocity profiles, pressure gradients, and the interplay between wave characteristics and non-Newtonian rheology. As a result, there is an urgent need for innovative modeling frameworks that can overcome these limitations and provide both accuracy and efficiency in predicting transport phenomena under peristaltic conditions. Recent advances in machine learning, particularly deep learning and physics-informed neural networks, offer an unprecedented opportunity to revolutionize the modeling of nonlinear transport processes. Machine learning has already demonstrated success in surrogate modeling, pattern recognition, and prediction of complex systems across fields such as turbulence modeling, multiphase flows, and biomedical diagnostics. However, its application to peristaltic transport of non-Newtonian fluids remains underexplored despite its potential to significantly enhance predictive capability while reducing reliance on oversimplified assumptions or computationally intensive simulations. The proposed invention addresses this gap by introducing a machine learning framework that integrates supervised learning with physics-informed constraints to model mass transport in non-Newtonian peristaltic systems. In contrast to black-box data-driven approaches that risk producing unphysical results, the invention embeds conservation laws of mass and momentum, rheological models, and boundary-driven wave dynamics directly into the learning architecture, ensuring predictions remain consistent with fundamental physics. Moreover, the framework leverages hybrid deep neural network designs, combining convolutional layers to extract spatial flow features, recurrent or temporal layers to capture dynamic evolution, and embedding strategies to incorporate governing equations, thereby offering both accuracy and generalization across diverse rheological and geometrical conditions. By learning from high-fidelity CFD simulations, experimental datasets, or a combination of both, the machine learning system can establish surrogate models that drastically reduce computational cost and enable real-time analysis, parameter optimization, and control strategies. This is particularly valuable in biomedical applications such as drug delivery, targeted therapy, and diagnostic modeling, where accurate understanding of solute transport under peristaltic motion in blood vessels, intestines, or other biological conduits is essential for designing effective treatment protocols. Similarly, in industrial contexts, peristaltic pumps handling polymer melts, suspensions, or food products benefit from predictive models that optimize mixing, dispersion, and throughput without requiring exhaustive simulations or empirical trial-and-error. Beyond predictive accuracy, the invention also advances interpretability through sensitivity analysis and feature importance extraction, which provide mechanistic insights into how parameters such as wave amplitude, wavelength, frequency, fluid rheological indices, and channel geometry influence solute dispersion and transport efficiency. This is a critical improvement over purely numerical simulations that, while producing detailed flow fields, often fail to yield transparent parameter-driven insights. Furthermore, the machine learning approach supports adaptability by continuously updating models with new data, making it possible to capture evolving conditions in biological systems or dynamic changes in industrial processes. In doing so, it bridges the gap between static offline modeling and dynamic real-time monitoring and control. The background of the proposed invention thus resides in addressing a longstanding challenge in fluid mechanics: the accurate and efficient modeling of nonlinear mass transport in peristaltic non-Newtonian systems, where existing methods remain either oversimplified or computationally prohibitive. By leveraging advances in artificial intelligence while maintaining physical consistency, the invention represents a paradigm shift that combines the strengths of physics-based modeling and data-driven learning. It not only overcomes the computational bottlenecks of CFD but also surpasses the limitations of reduced-order models that rely on heavy assumptions. Its multidisciplinary relevance spans biomedical engineering, pharmaceutical sciences, chemical and process engineering, microfluidics, and even soft robotics, wherever peristaltic-driven transport of complex fluids occurs. In essence, this invention emerges from the convergence of three critical needs: first, the demand for accurate modeling of non-Newtonian peristaltic transport in natural and industrial systems; second, the inefficiency of traditional analytical and numerical approaches in handling nonlinear, coupled dynamics at scale; and third, the transformative potential of machine learning to serve as a physics-informed surrogate modeling tool. By situating itself at this intersection, the invention provides a background rooted in decades of fluid mechanics research, while advancing into the frontier of computational intelligence, offering a solution that is both scientifically rigorous and practically impactful.

Summary of the proposed invention:

The present invention introduces a novel machine learning-based framework designed to accurately, efficiently, and robustly model mass transport in non-Newtonian fluids subjected to peristaltic motion, thereby addressing a longstanding gap between the limitations of conventional analytical and numerical approaches and the urgent demand for predictive, scalable, and adaptable solutions across biomedical, industrial, and microfluidic domains. At its core, the invention integrates data-driven learning with physics-informed constraints to capture the highly nonlinear and coupled dynamics of peristaltic transport, where traditional models often fail due to oversimplified assumptions or prohibitive computational expense. The framework employs hybrid deep neural network architectures that combine convolutional layers for spatial feature extraction, recurrent layers for capturing temporal evolution, and embedding layers for incorporating governing physical laws such as continuity and momentum conservation, as well as constitutive equations specific to non-Newtonian rheology. Unlike purely black-box machine learning models, which risk producing unphysical predictions, this invention ensures that embedded conservation principles and wave dynamics preserve fidelity to real-world transport behavior while simultaneously learning complex, high-dimensional relationships from data. The invention is capable of learning from diverse data sources, including high-fidelity computational fluid dynamics (CFD) simulations, experimental measurements, and in situ sensor data, which allows the models to generalize across a wide spectrum of flow regimes, geometrical configurations, and rheological properties, including shear-thinning, shear-thickening, viscoelastic, and yield-stress fluids. Once trained, the models serve as surrogate predictors that drastically reduce computational time compared to traditional CFD solvers, enabling real-time prediction, optimization, and control of peristaltic transport systems. This computational efficiency is particularly crucial for applications requiring dynamic adaptation, such as biomedical drug delivery in peristaltic organs like intestines and blood vessels, where time-sensitive predictions can directly influence therapeutic outcomes, or industrial peristaltic pumps handling complex suspensions and polymers, where real-time control optimizes mixing efficiency, energy consumption, and throughput. The invention also incorporates sensitivity analysis and explainability modules that quantify the influence of input parameters—such as wave amplitude, wavelength, frequency, fluid consistency index, flow index, Reynolds number, and channel geometry—on solute dispersion, mass transfer rates, and mixing efficiency, thereby providing mechanistic insights that surpass the black-box limitations of most machine learning models and enhance interpretability for end-users in engineering and biomedical domains. Furthermore, the system’s adaptive learning capability allows it to continually refine its predictive accuracy as new data becomes available, ensuring long-term reliability and adaptability to evolving conditions, such as changes in patient-specific physiological parameters or dynamic industrial processes. From a practical perspective, the invention is designed for modularity and scalability, enabling integration into existing process pipelines, microfluidic device designs, and biomedical diagnostic platforms. The machine learning framework can be deployed in cloud-based or edge-computing environments, supporting distributed data collection and real-time inference for both laboratory and field applications. In biomedical applications, for example, the invention can be used to non-invasively model nutrient absorption, drug dispersion, or diagnostic marker transport in peristaltic organs, offering clinicians a predictive tool that personalizes treatment protocols based on patient-specific rheological and physiological parameters. In industrial contexts, it offers plant operators an intelligent decision-support system that predicts system responses under varying operating conditions, thereby reducing downtime, minimizing waste, and improving efficiency. The invention also advances microfluidics by enabling the design of lab-on-a-chip systems that rely on peristaltic pumping of biofluids, where accurate modeling of non-Newtonian transport is critical to achieving reliable diagnostic and analytical results. The novelty of the invention lies not only in its technical approach—combining supervised learning, deep neural architectures, and physics-informed modeling—but also in its ability to bridge computational intelligence with classical fluid dynamics, offering a methodology that is both generalizable and domain-agnostic. While traditional perturbation-based analytical methods are constrained to limited parameter ranges and numerical methods face prohibitive computational demands, the proposed invention circumvents both by providing a surrogate model that is computationally light yet physically consistent. Additionally, unlike prior machine learning attempts in fluid dynamics that focus predominantly on Newtonian turbulence or laminar flows, this invention uniquely targets the complex, underexplored domain of non-Newtonian peristaltic transport, marking a transformative advancement in the field. The summary of the invention therefore emphasizes its potential to significantly accelerate scientific discovery and industrial innovation by offering researchers, engineers, and clinicians an accessible, efficient, and interpretable modeling tool. For researchers, it unlocks the ability to explore vast parameter spaces and test hypotheses without the burden of exhaustive simulations. For engineers, it delivers actionable predictions that can guide process optimization and device design. For clinicians, it provides predictive insights into physiological transport mechanisms critical for diagnostics and therapeutics. Beyond predictive modeling, the invention also facilitates optimization tasks by coupling the trained surrogate model with optimization algorithms, enabling automatic identification of optimal operating conditions for maximizing mixing efficiency, enhancing solute dispersion, or minimizing energy consumption in peristaltic transport systems. The adaptability of the invention further ensures cross-disciplinary applicability, extending from macro-scale industrial processes to micro-scale biomedical and microfluidic devices. Overall, the invention embodies a paradigm shift in fluid transport modeling by merging the rigor of physics-based laws with the flexibility and efficiency of artificial intelligence, thus creating a framework that is not only scientifically robust but also practically impactful across a diverse set of real-world applications.
Brief description of the proposed invention:

The proposed invention provides a comprehensive machine learning framework specifically designed for modeling mass transport phenomena in non-Newtonian fluids subjected to peristaltic motion, offering a unique combination of computational efficiency, physical consistency, and predictive accuracy that distinguishes it from existing analytical and numerical methods, and making it broadly applicable to biomedical, industrial, and microfluidic systems. The invention begins with the integration of input features that characterize the dynamics of peristaltic transport, including geometric parameters such as channel height, wavelength, and wave amplitude, fluid parameters such as consistency index, flow index, viscoelastic relaxation times, and yield stress, as well as flow parameters such as Reynolds number, Peclet number, and wave frequency. These features are processed by a hybrid deep neural network architecture that combines convolutional neural networks (CNNs) for spatial feature extraction with recurrent neural networks (RNNs), long short-term memory (LSTM) units, or gated recurrent units (GRUs) for capturing temporal evolution of flow and transport variables under periodic boundary-driven motion, while embedding physical constraints through physics-informed neural networks (PINNs) that ensure conservation of mass, momentum, and transport equations are inherently satisfied. The training process of the invention relies on a combination of high-fidelity CFD datasets, laboratory experimental data, and, where applicable, in vivo or in vitro biomedical data, ensuring that the model not only generalizes across different rheological regimes but also remains grounded in physical realism. The loss function of the neural network is formulated as a composite objective, balancing data-driven prediction errors with penalty terms enforcing compliance with governing equations, boundary conditions, and rheological models, thereby preventing unphysical predictions that are common in unconstrained machine learning approaches. Once trained, the invention functions as a surrogate model capable of rapidly predicting concentration distributions, velocity fields, dispersion coefficients, and solute transport efficiency under varying operating conditions, significantly reducing computational requirements compared to finite element or finite volume simulations. The invention further incorporates explainability and sensitivity analysis modules that decompose the contributions of different input features to the output predictions, thereby offering mechanistic insights into the dominant parameters influencing peristaltic transport, such as the interplay between wave frequency and shear-thinning rheology on dispersion efficiency or the impact of channel narrowing and yield stress on solute residence time. These interpretability features not only enhance the trustworthiness of the predictions but also support design optimization in industrial and biomedical contexts. Additionally, the invention is designed for adaptive learning, enabling it to incorporate new datasets in an online or incremental fashion without retraining from scratch, which ensures the framework remains accurate under evolving conditions, such as patient-specific variations in physiological flows, aging effects in biological fluids, or dynamic changes in industrial process conditions. The invention also supports deployment across different computational environments, including cloud-based servers for large-scale training, edge devices for real-time monitoring, and embedded systems for integration into medical diagnostic tools or industrial controllers. For biomedical applications, the invention provides predictive models of drug delivery, nutrient absorption, and diagnostic biomarker transport in organs exhibiting peristaltic motion, enabling clinicians to simulate patient-specific responses and optimize treatment protocols. In industrial applications, it serves as a decision-support tool for peristaltic pumps transporting complex suspensions, emulsions, or polymeric fluids, where accurate predictions of flow uniformity, dispersion efficiency, and mixing are critical for quality assurance and process optimization. In microfluidic systems, the invention facilitates the design and control of lab-on-a-chip devices where peristaltic micropumps handle biological samples, ensuring reproducibility and efficiency in diagnostic assays. The invention’s novelty lies in its synergistic integration of machine learning and fluid physics, which provides computational acceleration, physical rigor, and adaptability that surpasses traditional models. Unlike analytical methods that are limited to restrictive approximations, and unlike CFD simulations that demand high computational resources, the invention offers real-time predictive capability, making it especially suitable for dynamic, real-world applications. Furthermore, the invention establishes a modular workflow: (i) preprocessing modules for normalizing and encoding input features, (ii) core predictive modules based on hybrid deep networks with embedded physics, (iii) postprocessing modules that generate interpretable outputs including dispersion coefficients, solute residence times, and efficiency metrics, and (iv) optimization modules that couple surrogate predictions with optimization algorithms to identify operating conditions that maximize performance. This modularity ensures that the invention can be tailored to specific domains, whether predicting glucose absorption in the small intestine, monitoring drug dispersion in blood vessels, or controlling flow in a peristaltic micro-pump for analytical chemistry. The robustness of the invention is further enhanced through uncertainty quantification modules that estimate confidence intervals for predictions, ensuring that users are provided with reliability measures critical in safety-sensitive domains such as healthcare and pharmaceutical engineering. The invention thus represents not merely a computational model, but a comprehensive intelligent platform for understanding, predicting, and optimizing mass transport in non-Newtonian peristaltic systems. By merging physical laws with adaptive learning, the invention achieves a balance of accuracy, speed, and interpretability that has not been achieved by prior methods, and its wide applicability across physiological, industrial, and microfluidic scales makes it a transformative advancement in the field of fluid transport modeling. , Claims:1.A machine learning framework for modeling mass transport in non-Newtonian fluids under peristaltic motion, comprising:
a.a hybrid neural network architecture integrating convolutional layers for spatial feature extraction and recurrent layers for temporal dynamics;
b.a physics-informed module embedding conservation of mass, momentum, and constitutive equations of non-Newtonian rheology;
c.a training process utilizing high-fidelity simulation data and experimental measurements to generate predictive models of solute transport.

2.The framework of claim 1, wherein the non-Newtonian fluid behavior includes shear-thinning, shear-thickening, viscoelasticity, and yield stress characteristics.

3.The framework of claim 1, wherein the physics-informed module applies penalty functions to the loss function to enforce boundary conditions, wave dynamics, and governing equations.

4.The framework of claim 1, further comprising an explainability and sensitivity analysis module configured to identify dominant parameters such as wave amplitude, frequency, wavelength, Reynolds number, and rheological indices affecting solute transport.

5.The framework of claim 1, wherein the trained model operates as a surrogate predictor capable of reducing computational time compared to finite element or finite volume simulations while maintaining physical consistency.

6.The framework of claim 1, wherein the invention is adaptable for real-time monitoring and control of biomedical peristaltic systems including drug delivery, nutrient absorption, and blood transport.

7.The framework of claim 1, wherein the invention is configured for industrial peristaltic pumps transporting suspensions, emulsions, or polymeric fluids, enabling prediction and optimization of mixing efficiency and throughput.

8.The framework of claim 1, wherein the invention supports microfluidic applications by modeling peristaltic pumping of biological samples in lab-on-a-chip devices for diagnostics and analytical chemistry.

9.The framework of claim 1, further comprising adaptive learning capability that updates the model incrementally with new experimental or simulation data without requiring complete retraining.

10.The framework of claim 1, further comprising uncertainty quantification modules configured to provide confidence intervals for predicted velocity fields, dispersion coefficients, and solute concentration distributions.