arXiv subjects

Mohammad Kohandel

Publications and source records attributed to Mohammad Kohandel.

At least 19 recordsLinked to original sources

arXiv2026

Parallel Scan Recurrent Neural Quantum States for Scalable Variational Monte Carlo

Neural-network quantum states have emerged as a powerful variational framework for quantum many-body systems, with recent progress often driven by massively parallel architectures such as transformers. Recurrent neural network quantum states, however, are frequently regarded as intrinsically sequential and therefore less scalable. Here we revisit this view by showing that modern recurrent architectures can support fast, accurate, and computationally accessible neural quantum state simulations. Using autoregressive recurrent wave functions together with recent advances in parallelizable recurrence, we develop variational ans\"atze, called parallel scan recurrent neural quantum states (PSR-NQS), which can be trained efficiently within variational Monte Carlo in one and two spatial dimensions. We demonstrate accurate benchmark results and show that, with iterative retraining, our approach reaches two-dimensional spin lattices as large as $52\times52$ while remaining in agreement with available quantum Monte Carlo data. Our results establish recurrent architectures as a practical and promising route toward scalable neural quantum state simulations with modest computational resources.

cond-mat.str-el↗

arXiv2026

Private and interpretable clinical prediction with quantum-inspired tensor train models

Publicly available clinical machine learning models pose an underappreciated privacy risk: their parameters or outputs can be exploited to recover information from patients whose data were used during training. Moreover, this risk is exacerbated by models such as logistic regression (LR), which are typically preferred in clinical settings for their transparency. To assess this empirically, we attack LORIS, a publicly available LR model for immunotherapy response prediction hosted on a U.S. government website. From evaluations through its public interface, we recover the model parameters and identify the training cohort with high confidence. More broadly, we design cohort-level membership inference attacks under three levels of adversarial access---binary black-box, continuous black-box, and white-box---and apply them to both LR models and shallow neural networks (NNs) trained on the same task. Our results reveal that even a cohort of 35 patients can be reliably identified within training sets of hundreds to thousands, and that common practices such as cross-validation amplify rather than mitigate this risk. To address these vulnerabilities, we propose a quantum-inspired defense based on tensorizing discretized models into tensor trains (TTs). This representation obfuscates model parameters and preserves accuracy, while offering black-box protection comparable to practical Differential Privacy baselines. Additionally, the TT representations retain LR interpretability and extend it through efficient computation of marginal and conditional distributions, enabling this richer analysis also for black-box models such as NNs. Our results establish tensorization as a practical, post-hoc tool for private, interpretable, and effective clinical prediction.

cs.LG↗

arXiv2025

Integrating Mechanistic Modeling and Machine Learning to Study CD4+/CD8+ CAR-T Cell Dynamics with Tumor Antigen Regulation

Chimeric antigen receptor (CAR) T cell therapy has shown remarkable success in hematological malignancies, yet patient responses remain highly variable and the roles of CD4+ and CD8+ subsets are not fully understood. We present an extended mathematical framework of CAR-T cell dynamics that explicitly models CD4+ helper and CD8+ cytotoxic lineages and their interactions with tumor antigen burden. Building on the Kirouac et al. (2023) model of antigen-regulated memory-effector-exhaustion transitions, our system of differential equations incorporates CD4-mediated modulation of CD8+ proliferation, cytotoxicity, and memory regeneration through biologically grounded, saturating interactions. Sensitivity analyses identify effector proliferation, antigen turnover, and CD8+ expansion rates as dominant drivers of treatment outcome. Virtual patient simulations recover reported qualitative trends in CAR-T composition, including enhanced expansion and tumor clearance for defined CD4:CD8 products relative to CD8-only formulations, while also revealing inter-patient variability and time-dependent effects. To assess the practical limits of patient-level prediction under parameter uncertainty, we introduce controlled noise into key parameters and show that direct mechanistic classification rapidly degrades. We then demonstrate that a simple feed-forward neural network can partially recover predictive signal from noisy inputs, outperforming a naive baseline while remaining consistent with mechanistic sensitivities. This work positions the extended model as a hypothesis generator, and illustrates how data-driven methods can complement mechanistic modeling when parameter uncertainty constrains predictive confidence.

q-bio.QM↗

arXiv2025

IP-Basis PINNs: Efficient Multi-Query Inverse Parameter Estimation

Solving inverse problems with Physics-Informed Neural Networks (PINNs) is computationally expensive for multi-query scenarios, as each new set of observed data requires a new, expensive training procedure. We present Inverse-Parameter Basis PINNs (IP-Basis PINNs), a meta-learning framework that extends the foundational work of Desai et al. (2022) to enable rapid and efficient inference for inverse problems. Our method employs an offline-online decomposition: a deep network is first trained offline to produce a rich set of basis functions that span the solution space of a parametric differential equation. For each new inverse problem online, this network is frozen, and solutions and parameters are inferred by training only a lightweight linear output layer against observed data. Key innovations that make our approach effective for inverse problems include: (1) a novel online loss formulation for simultaneous solution reconstruction and parameter identification, (2) a significant reduction in computational overhead via forward-mode automatic differentiation for PDE loss evaluation, and (3) a non-trivial validation and early-stopping mechanism for robust offline training. We demonstrate the efficacy of IP-Basis PINNs on three diverse benchmarks, including an extension to universal PINNs for unknown functional terms-showing consistent performance across constant and functional parameter estimation, a significant speedup per query over standard PINNs, and robust operation with scarce and noisy data.

cs.LG↗

arXiv2025

A Unified Framework for Simultaneous Parameter and Function Discovery in Differential Equations

Inverse problems involving differential equations often require identifying unknown parameters or functions from data. Existing approaches, such as Physics-Informed Neural Networks (PINNs), Universal Differential Equations (UDEs) and Universal Physics-Informed Neural Networks (UPINNs), are effective at isolating either parameters or functions but can face challenges when applied simultaneously due to solution non-uniqueness. In this work, we introduce a framework that addresses these limitations by establishing conditions under which unique solutions can be guaranteed. To illustrate, we apply it to examples from biological systems and ecological dynamics, demonstrating accurate and interpretable results. Our approach significantly enhances the potential of machine learning techniques in modeling complex systems in science and engineering.

cs.LG↗

arXiv2024

Enhancing Symbolic Regression and Universal Physics-Informed Neural Networks with Dimensional Analysis

In engineering and applied mathematics, developing accurate mathematical models to predict and understand real-world phenomena is of utmost importance. Symbolic regression is a useful machine learning-based tool to fit models but it can be computationally expensive. We present a new method for enhancing symbolic regression for differential equations via dimensional analysis, specifically the Buckingham $\Pi$ theorem and Ipsen's method. Since symbolic regression often suffers from high computational costs and overfitting, nondimensionalizing datasets reduces the number of input variables, simplifies the search space, and ensures that derived equations are physically meaningful. As a first step, we combine dimensional analysis with the PySR symbolic regression algorithm to show that dimensional analysis improves the accuracy of recovering algebraic equations. The results demonstrate that transforming data into a dimensionless form significantly improves the training and test error of the symbolic expressions found. Then, as our main contribution, we perform nondimensionalization guided by Ipsen's method. We then incorporate the nondimensionalized equation into a pipeline combining Universal Physics-Informed Neural Networks and symbolic regression to recover the unknown term when a differential equation is only partially known. We find that symbolic regression is able to better recover the unknown term after nondimensionalizing the data, under both noisy and noiseless conditions. These findings suggest that integrating dimensional analysis with symbolic regression can significantly lower computational costs and increase accuracy, providing a robust framework for automated discovery of governing equations in complex systems when data is limited.

cs.LG↗

arXiv2024

Conformalized Physics-Informed Neural Networks

Physics-informed neural networks (PINNs) are an influential method of solving differential equations and estimating their parameters given data. However, since they make use of neural networks, they provide only a point estimate of differential equation parameters, as well as the solution at any given point, without any measure of uncertainty. Ensemble and Bayesian methods have been previously applied to quantify the uncertainty of PINNs, but these methods may require making strong assumptions on the data-generating process, and can be computationally expensive. Here, we introduce Conformalized PINNs (C-PINNs) that, without making any additional assumptions, utilize the framework of conformal prediction to quantify the uncertainty of PINNs by providing intervals that have finite-sample, distribution-free statistical validity.

cs.LG↗

arXiv2024

Learning Chemotherapy Drug Action via Universal Physics-Informed Neural Networks

Quantitative systems pharmacology (QSP) is widely used to assess drug effects and toxicity before the drug goes to clinical trial. However, significant manual distillation of the literature is needed in order to construct a QSP model. Parameters may need to be fit, and simplifying assumptions of the model need to be made. In this work, we apply Universal Physics-Informed Neural Networks (UPINNs) to learn unknown components of various differential equations that model chemotherapy pharmacodynamics. We learn three commonly employed chemotherapeutic drug actions (log-kill, Norton-Simon, and E_max) from synthetic data. Then, we use the UPINN method to fit the parameters for several synthetic datasets simultaneously. Finally, we learn the net proliferation rate in a model of doxorubicin (a chemotherapeutic) pharmacodynamics. As these are only toy examples, we highlight the usefulness of UPINNs in learning unknown terms in pharmacodynamic and pharmacokinetic models.

q-bio.QM↗

arXiv2024

Denoising Diffusion Restoration Tackles Forward and Inverse Problems for the Laplace Operator

Diffusion models have emerged as a promising class of generative models that map noisy inputs to realistic images. More recently, they have been employed to generate solutions to partial differential equations (PDEs). However, they still struggle with inverse problems in the Laplacian operator, for instance, the Poisson equation, because the eigenvalues that are large in magnitude amplify the measurement noise. This paper presents a novel approach for the inverse and forward solution of PDEs through the use of denoising diffusion restoration models (DDRM). DDRMs were used in linear inverse problems to restore original clean signals by exploiting the singular value decomposition (SVD) of the linear operator. Equivalently, we present an approach to restore the solution and the parameters in the Poisson equation by exploiting the eigenvalues and the eigenfunctions of the Laplacian operator. Our results show that using denoising diffusion restoration significantly improves the estimation of the solution and parameters. Our research, as a result, pioneers the integration of diffusion models with the principles of underlying physics to solve PDEs.

cs.LG↗

arXiv2022

A PINN Approach to Symbolic Differential Operator Discovery with Sparse Data

Given ample experimental data from a system governed by differential equations, it is possible to use deep learning techniques to construct the underlying differential operators. In this work we perform symbolic discovery of differential operators in a situation where there is sparse experimental data. This small data regime in machine learning can be made tractable by providing our algorithms with prior information about the underlying dynamics. Physics Informed Neural Networks (PINNs) have been very successful in this regime (reconstructing entire ODE solutions using only a single point or entire PDE solutions with very few measurements of the initial condition). We modify the PINN approach by adding a neural network that learns a representation of unknown hidden terms in the differential equation. The algorithm yields both a surrogate solution to the differential equation and a black-box representation of the hidden terms. These hidden term neural networks can then be converted into symbolic equations using symbolic regression techniques like AI Feynman. In order to achieve convergence of these neural networks, we provide our algorithms with (noisy) measurements of both the initial condition as well as (synthetic) experimental data obtained at later times. We demonstrate strong performance of this approach even when provided with very few measurements of noisy data in both the ODE and PDE regime.

cs.LG↗

arXiv2021

SARS-CoV-2 quantum sensor based on nitrogen-vacancy centers in diamond

The development of highly sensitive and rapid biosensing tools targeted to the highly contagious virus SARS-CoV-2 is critical to tackling the COVID-19 pandemic. Quantum sensors can play an important role, thanks to their superior sensitivity and fast improvements in recent years. Here we propose a molecular transducer designed for nitrogen-vacancy (NV) centers in nanodiamonds, translating the presence of SARS-CoV-2 RNA into an unambiguous magnetic noise signal that can be optically read out. We evaluate the performance of the hybrid sensor, including its sensitivity and false negative rate, and compare it to widespread diagnostic methods. The proposed method is fast and promises to reach a sensitivity down to a few hundreds of RNA copies with false negative rate less than 1%. The proposed hybrid sensor can be further implemented with different solid-state defects and substrates, generalized to diagnose other RNA viruses, and integrated with CRISPR technology.

quant-ph↗

arXiv2016

Phenotypic heterogeneity in modeling cancer evolution

The unwelcome evolution of malignancy during cancer progression emerges through a selection process in a complex heterogeneous population structure. In the present work, we investigate evolutionary dynamics in a phenotypically heterogeneous population of stem cells (SCs) and their associated progenitors. The fate of a malignant mutation is determined not only by overall stem cell and differentiated cell growth rates but also differentiation and dedifferentiation rates. We investigate the effect of such a complex population structure on the evolution of malignant mutations. We derive exact analytic results for the fixation probability of a mutant arising in each of the subpopulations. The analytic results are in almost perfect agreement with the numerical simulations. Moreover, a condition for evolutionary advantage of a mutant cell versus the wild type population is given in the present study. We also show that microenvironment-induced plasticity in invading mutants leads to more aggressive mutants with higher fixation probability. Our model predicts that decreasing polarity between stem and differentiated cells turnover would raise the survivability of non-plastic mutants; while it would suppress the development of malignancy for plastic mutants. We discuss our model in the context of colorectal/intestinal cancer (at the epithelium). This novel mathematical framework can be applied more generally to a variety of problems concerning selection in heterogeneous populations, in other contexts such as population genetics, and ecology.

q-bio.PE↗

arXiv2015

Modelling Invasion Dynamics with Spatial Random-Fitness due to Microenvironment

Numerous experimental studies have demonstrated that the microenvironment is a key regulator influencing the proliferative and migrative potentials of species. Spatial and temporal disturbances lead to adverse and hazardous microenvironments for cellular systems that is reflected in the phenotypic heterogeneity within the system. In this paper, we study the effect of microenvironment on the invasive capability of species, or mutants, on structured grids under the influence of site-dependent random proliferation in addition to a migration potential. We discuss both continuous and discrete fitness distributions. Our results suggest that the invasion probability is negatively correlated with the variance of fitness distribution of mutants (for both advantageous and neutral mutants) in the absence of migration of both types of cells. A similar behaviour is observed even in the presence of a random fitness distribution of host cells in the system with neutral fitness rate. In the case of a bimodal distribution, we observe zero invasion probability until the system reaches a (specific) proportion of advantageous phenotypes. Also, we find that the migrative potential amplifies the invasion probability as the variance of fitness of mutants increases in the system, which is the exact opposite in the absence of migration. Our computational framework captures the harsh microenvironmental conditions through quenched random fitness distributions and migration of cells, and our analysis shows that they play an important role in the invasion dynamics of several biological systems such as bacterial micro-habitats, epithelial dysplasia, and metastasis. We believe that our results may lead to more experimental studies, which can in turn provide further insights into the role and impact of heterogeneous environments on invasion dynamics.

q-bio.PE↗

arXiv2014

The duality of spatial death-birth and birth-death processes and limitations of the isothermal theorem

Evolutionary models on graphs, as an extension of the Moran process, have two major implementations: birth-death (BD) models (or the invasion process) and death- birth (DB) models (or voter models). The isothermal theorem states that the fixation probability of mutants in a large group of graph structures (known as isothermal graphs, which include regular graphs) coincides with that for the mixed population. This result has been proven by Lieberman et al (Nature 433: 312-316, 2005) in the case of BD processes, where mutants differ from the wild types by their birth rate (and not by their death rate). In this paper we discuss to what extent the isothermal theorem can be formulated for DB processes, proving that it only holds for mutants that differ from the wild type by their death rate (and not by their birth rate). For more general BD and DB processes with arbitrary birth and death rates of mutants, we show that the fixation probabilities of mutants are different from those obtained in the mass-action populations. We focus on spatial lattices and show that the difference between BD and DB processes on 1D and 2D lattices are non-small even for large population sizes. We support these results with a generating function approach that can be generalized to arbitrary graph structures. Finally, we discuss several biological applications of the results.

q-bio.QM↗

arXiv2014

Replicator Dynamics of of Cancer Stem Cell; Selection in the Presence of Differentiation and Plasticity

Stem cells have the potential to produce lineages of non-stem cell populations (differentiated cells) via a ubiquitous hierarchal division scheme. Differentiation of a stem cell into (partially) differentiated cells can happen either symmetrically or asymmetrically. The selection dynamics of a mutant cancer stem cell should be investigated in the light of a stem cell proliferation hierarchy and presence of a non-stem cell population. By constructing a three-compartment Moran-type model composed of normal stem cells, mutant (cancer) stem cells and differentiated cells, we derive the replicator dynamics of stem cell frequencies where asymmetric differentiation and differentiated cell death rates are included in the model. We determine how these new factors change the conditions for a successful mutant invasion and discuss the variation on the steady state fraction of the population as different model parameters are changed. By including the phenotypic plasticity/dedifferentiation, in which a progenitor/differentiated cell can transform back into a cancer stem cell, we show that the effective fitness of mutant stem cells is not only determined by their proliferation and death rates but also according to their dedifferentiation potential. By numerically solving the model we derive the phase diagram of the advantageous and disadvantageous phases of cancer stem cells in the space of proliferation and dedifferentiation potentials. The result shows that at high enough dedifferentiation rates even a previously disadvantageous mutant can take over the population of normal stem cells. This observation has implications in different areas of cancer research including experimental observations that imply metastatic cancer stem cell types might have lower proliferation potential than other stem cell phenotypes while showing much more phenotypic plasticity and can undergo clonal expansion.

q-bio.CB↗

arXiv2014

Modeling Age-Dependent Radiation-Induced Second Cancer Risks and Estimation of Mutation Rate: An Evolutionary Approach

Although the survival rate of cancer patients has significantly increased due to advances in anti-cancer therapeutics, one of the major side effects of these therapies, particularly radiotherapy, is the potential manifestation of radiation-induced secondary malignancies. In this work, a novel evolutionary stochastic model is introduced that couples short-term formalism (during radiotherapy) and long-term formalism (post treatment). This framework is used to estimate the risks of second cancer as a function of spontaneous background and radiation-induced mutation rates of normal and pre-malignant cells. By fitting the model to available clinical data for spontaneous background risk together with data of Hodgkins lymphoma survivors (for various organs), the second cancer mutation rate is estimated. The model predicts a significant increase in mutation rate for some cancer types, which may be a sign of genomic instability. Finally, it is shown that the model results are in agreement with the measured results for excess relative risk (ERR) as a function of exposure age, and that the model predicts a negative correlation of ERR with increase in attained age. This novel approach can be used to analyze several radiotherapy protocols in current clinical practice, and to forecast the second cancer risks over time for individual patients.

q-bio.QM↗

arXiv2013

Stochastic Model for Tumor Control Probability: Effects of Cell Cycle and (A)symmetric Proliferation

Estimating the required dose in radiotherapy is of crucial importance since the administrated dose should be sufficient to eradicate the tumor and at the same time should inflict minimal damage on normal cells. The probability that a given dose and schedule of ionizing radiation eradicates all the tumor cells in a given tissue is called the tumor control probability (TCP), and is often used to compare various treatment strategies used in radiation therapy. In this paper, we aim to investigate the effects of including cell-cycle phase on the TCP by analyzing a stochastic model of a tumor comprised of actively dividing cells and quiescent cells with different radiation sensitivities. We derive an exact phase-diagram for the steady-state TCP of the model and show that at high, clinically-relevant doses of radiation, the distinction between active and quiescent tumor cells (i.e. accounting for cell-cycle effects) becomes of negligible importance in terms of its effect on the TCP curve. However, for very low doses of radiation, these proportions become significant determinants of the TCP. Moreover, we use a novel numerical approach based on the method of characteristics for partial differential equations, validated by the Gillespie algorithm, to compute the TCP as a function of time. We observe that our results differ from the results in the literature using similar existing models, even though similar parameters values are used, and the reasons for this are discussed.

q-bio.QM↗

arXiv2003

Disorder-Driven Magnetic Field Dependence of the Internal Field Distribution in the Bragg Glass Phase of Type-II Superconductors

We use the replica variational method to study the effects of weak point disorder on the variance of the internal field distribution measured in NMR and muon-spin rotation experiments in type-II superconductors. We show that for a simple model there is significant magnetic field dependence which is extrinsic and disorder-driven, and does not have a microscopic (non $s-$wave pairing) origin. Results are presented where we examine the dependence of the magnetic field variance upon the strength of the applied external field.

cond-mat.dis-nn↗