arXiv subjects

Sumit Sinha

Publications and source records attributed to Sumit Sinha.

At least 19 recordsLinked to original sources

arXiv2026

LieStoNet: Learning Lie Symmetries from Spatiotemporal Data for Stochastic Dynamical Systems

Symmetry is central to modern machine learning and physics: invariances and equivariances improve sample efficiency, robustness, and out-of-distribution generalization, while symmetry principles guide scientific modeling. Yet for stochastic dynamical systems the relevant continuous symmetries are rarely known, and symmetry discovery for SDEs has remained essentially unexplored. We introduce \textit{LieStoNet}, an end-to-end, \emph{template-free} framework for discovering Lie-point symmetries of SDEs directly from spatiotemporal trajectories, without prespecifying symmetry groups, templates, or canonical coordinates. Building on the seminal SDE Lie-symmetry theory of Gaeta and Quintero (1999), which formalizes Lie-point SDE symmetries and their relation to Fokker-Planck symmetries, LieStoNet learns neural surrogates for drift and diffusion from increments, then learns projectable generators by enforcing the SDE determining equations, separately regularizing for closure under Lie brackets, adherence to the Lie algebra axioms (bilinearity, antisymmetry, Jacobi), and a non-redundant independent basis. The surrogate also defines an associated Fokker-Planck equation, enabling optional discovery of its Lie-point symmetries in parallel. Across multiple canonical SDEs with known analytic symmetries, LieStoNet recovers generators consistent with the ground-truth symmetry algebra, providing interpretable symmetry discovery for noisy dynamics. Code is available at \href{https://github.com/sumit-sinha-seas/LieStoNet_Final.git}{this link}.

cond-mat.stat-mech↗

arXiv2026

Generative optimal transport via forward-backward HJB matching

Controlling the evolution of a many-body stochastic system from a disordered reference state to a structured target ensemble, characterized empirically through samples, arises naturally in non-equilibrium statistical mechanics and stochastic control. The natural relaxation of such a system - driven by diffusion - runs from the structured target toward the disordered reference. The natural question is then: what is the minimum-work stochastic process that reverses this relaxation, given a pathwise cost functional combining spatial penalties and control effort? Computing this optimal process requires knowledge of trajectories that already sample the target ensemble - precisely the object one is trying to construct. We resolve this by establishing a time-reversal duality: the value function governing the hard backward dynamics satisfies an equivalent forward-in-time HJB equation, whose solution can be read off directly from the tractable forward relaxation trajectories. Via the Cole-Hopf transformation and its associated Feynman-Kac representation, this forward potential is computed as a path-space free energy averaged over these forward trajectories - the same relaxation paths that are easy to simulate - without any backward simulation or knowledge of the target beyond samples. The resulting framework provides a physically interpretable description of stochastic transport in terms of path-space free energy, risk-sensitive control, and spatial cost geometry. We illustrate the theory with numerical examples that visualize the learned value function and the induced controlled diffusions, demonstrating how spatial cost fields shape transport geometry analogously to Fermat's Principle in inhomogeneous media. Our results establish a unifying connection between stochastic optimal control, Schr\"odinger bridge theory, and non-equilibrium statistical mechanics.

cond-mat.stat-mech↗

arXiv2026

Morphological instability of an invasive active-passive interface

Morphological instabilities of growing tissues that impinge on passive materials are typical of invasive cancers. To explain these instabilities in experiments on breast epithelial spheroids in an extracellular matrix, we develop a continuum phase field model of a growing active liquid expanding into a passive viscoelastic matrix. Linear stability analysis of the sharp-interface limit of the governing equations predicts that the tissue interface can develops long-wavelength instabilities, but these instabilities are suppressed when the active carcinoid is embedded in an elastic matrix. We develop a theoretical morphological phase diagram, and complement these with two-dimensional finite element (FEM) phase-field simulations to track the nonlinear evolution of the interface with results consistent with theoretical predictions and experimental observations. Our study provides a basis for the emergence of interfacial instabilities in active-passive systems with the potential to control them.

cond-mat.soft↗

arXiv2025

Controlling the morphologies and dynamics in three-dimensional tissues

A number of factors, such as, cell-cell interactions and self-propulsion of cells driven by cytoskeletal forces determine tissue morphologies and dynamics. To explore the interplay between these factors in controlling the dynamics at the tissue scale, we created a minimal three dimensional model in which short-range repulsive elastic forces account for cell-cell interactions. Self-propulsion is modeled as active uncorrelated random stochastic forces, with strength $\mu$, that act on individual cells and is the only source of cell motility. Strikingly, variations in polydispersity in cell sizes ($\Sigma$) and cell elasticity ($E$), results in the formation of a variety of distinct ``phases", driven entirely by $\mu$. At low $E$, the tissue behaves like a liquid, at all values of $\Sigma$, whereas at high $E$ and $\Sigma$, it has the characteristics of a glass. The tissue crystallizes at low $\Sigma$ provided $E$ exceeds a critical value. Over a narrow range of $E$ and $\Sigma$, that lies between the boundaries of the liquid and glass phase, the effective viscosity increases like in a glass as the cell density increases and saturates as the cells are compressed beyond a certain value, creating the viscosity saturation (VS) phase. The VS phase does not form in systems at finite temperature in which the dynamics satisfies the Fluctuation Dissipation Theorem. In the glass phase, the tissue exhibits aging (relaxation times depend on the waiting time) behavior at high $E$ values. Our findings provide a framework for designing tissues with tunable material properties by controlling the physical characteristics of cells.

cond-mat.soft↗

arXiv2024

Hamiltonian bridge: A physics-driven generative framework for targeted pattern control

Patterns arise spontaneously in a range of systems spanning the sciences, and their study typically focuses on mechanisms to understand their evolution in space-time. Increasingly, there has been a transition towards controlling these patterns in various functional settings, with implications for engineering. Here, we combine our knowledge of a general class of dynamical laws for pattern formation in non-equilibrium systems, and the power of stochastic optimal control approaches to present a framework that allows us to control patterns at multiple scales, which we dub the "Hamiltonian bridge". We use a mapping between stochastic many-body Lagrangian physics and deterministic Eulerian pattern forming PDEs to leverage our recent approach utilizing the Feynman-Kac-based adjoint path integral formulation for the control of interacting particles and generalize this to the active control of patterning fields. We demonstrate the applicability of our computational framework via numerical experiments on the control of phase separation with and without a conserved order parameter, self-assembly of fluid droplets, coupled reaction-diffusion equations and finally a phenomenological model for spatio-temporal tissue differentiation. We interpret our numerical experiments in terms of a theoretical understanding of how the underlying physics shapes the geometry of the pattern manifold, altering the transport paths of patterns and the nature of pattern interpolation. We finally conclude by showing how optimal control can be utilized to generate complex patterns via an iterative control protocol over pattern forming pdes which can be casted as gradient flows. All together, our study shows how we can systematically build in physical priors into a generative framework for pattern control in non-equilibrium systems across multiple length and time scales.

cond-mat.soft↗

arXiv2024

Proliferation-driven mechanical feedback regulates cell dynamics in growing tissues

Local stresses in a tissue, a collective property, regulate cell division and apoptosis. In turn, cell growth and division induce active stresses in the tissue. As a consequence, there is a feedback between cell growth and local stresses. However, how the cell dynamics depend on local stress-dependent cell division and the feedback strength is not fully understood. Here, we probe the consequences of stress-mediated growth and cell division on cell dynamics using agent-based simulations of a two-dimensional growing tissue. We discover a rich dynamical behavior of individual cells, ranging from jamming (mean square displacement, $\Delta (t) \sim t^{\alpha}$ with $\alpha$ less than unity), to hyperdiffusion ($\alpha > 2$) depending on cell division rate and the strength of the mechanical feedback. Strikingly, $\Delta (t)$ is determined by the tissue growth law, which quantifies cell proliferation (number of cells $N(t)$ as a function of time). The growth law ($N(t) \sim t^{\lambda}$ at long times) is regulated by the critical pressure that controls the strength of the mechanical feedback and the ratio between cell division-apoptosis rates. We show that $\lambda \sim \alpha$, which implies that higher growth rate leads to a greater degree of cell migration. The variations in cell motility are linked to the emergence of highly persistent forces extending over several cell cycle times. Our predictions are testable using cell-tracking imaging techniques.

cond-mat.soft↗

arXiv2023

On the role of mechanical feedback in synchronous to asynchronous transition during embryogenesis

Experiments have shown that during the initial stage of Zebrafish morphogenesis a synchronous to asynchronous transition (SAT) occurs, as the cells divide extremely rapidly. In the synchronous phase, the cells divide in unison unlike in the asynchronous phase. Despite the widespread observation of SAT in experiments, a theory to calculate the critical number of cell cycles, $n^{*}$, at which asynchronous growth emerges does not exist. Here, using a model for the cell cycle, with the assumption that cell division times are Gaussian distributed with broadening, we predict $n^{*}$ and the time at which the SAT occurs. The theoretical results are in excellent agreement with experiments. The theory, supplemented by agent based simulations, establish that the SAT emerges as a consequence of biomechanical feedback on cell division. The emergence of asynchronous phase is due to linearly increasing fluctuations in the cell cycle times with each round of cell division. We also make several testable predictions, which would further shed light on the role of biomechanical feedback on the growth of multicellular systems.

physics.bio-ph↗

arXiv2023

Optimal control of interacting active particles on complex landscapes

Active many-body systems composed of many interacting degrees of freedom often operate out of equilibrium, giving rise to non-trivial emergent behaviors which can be functional in both evolved and engineered contexts. This naturally suggests the question of control to optimize function. Using navigation as a paradigm for function, we deploy the language of stochastic optimal control theory to formulate the inverse problem of shepherding a system of interacting active particles across a complex landscape. We implement a solution to this high-dimensional problem using an Adjoint-based Path Integral Control (APIC) algorithm that combines the power of recently introduced continuous-time back-propagation methods and automatic differentiation with the classical Feynman-Kac path integral formulation in statistical mechanics. Numerical experiments for controlling individual and interacting particles in complex landscapes show different classes of successful navigation strategies as a function of landscape complexity, as well as the intrinsic noise and drive of the active particles. However, in all cases, we see the emergence of paths that correspond to traversal along the edges of ridges and ravines, which we can understand using a variational analysis. We also show that the work associated with optimal strategies is inversely proportional to the length of the time horizon of optimal control, a result that follows from scaling considerations. All together, our approach serves as a foundational framework to control active non-equilibrium systems optimally to achieve functionality, embodied as a path on a high-dimensional manifold.

cond-mat.soft↗

arXiv2022

Topological transitions, turbulent-like motion and long-time-tails driven by cell division in biological tissues

The complex spatiotemporal flow patterns in living tissues, driven by active forces, have many of the characteristics associated with inertial turbulence even though the Reynolds number is extremely low. Analyses of experimental data from two-dimensional epithelial monolayers in combination with agent-based simulations show that cell division and apoptosis lead to directed cell motion for hours, resulting in rapid topological transitions in neighboring cells. These transitions in turn generate both long ranged and long lived clockwise and anticlockwise vortices, which gives rise to turbulent-like flows. Both experiments and simulations show that at long wavelengths the wave vector ($k$) dependent energy spectrum $E(k) \approx k^{-5/3}$, coinciding with the Kolmogorov scaling in fully developed inertial turbulence. Using theoretical arguments and simulations, we show that long-lived vortices lead to long-time tails in the velocity auto-correlation function, $C_v(t) \sim t^{-1/2}$, which has the same structure as in classical 2D fluids but with a different scaling exponent.

cond-mat.soft↗

arXiv2022

Free volume theory explains the unusual behavior of viscosity in a non-confluent tissue during morphogenesis

A recent experiment on zebrafish blastoderm morphogenesis showed that the viscosity ({\eta}) of a non-confluent embryonic tissue grows sharply until a critical cell packing fraction ({\phi}S). The increase in {\eta} up to {\phi}S is similar to the behavior observed in several glass-forming materials, which suggests that the cell dynamics is sluggish or glass-like. Surprisingly, {\eta} is a constant above {\phi}S. To determine the mechanism of this unusual dependence of {\eta} on {\phi}, we performed extensive simulations using an agent-based model of a dense non-confluent two-dimensional tissue. We show that polydispersity in the cell size, and the propensity of the cells to deform, results in the saturation of the available free area per cell beyond a critical packing fraction. Saturation in the free space not only explains the viscosity plateau above {\phi}S but also provides a relationship between equilibrium geometrical packing to the dramatic increase in the relaxation dynamics.

cond-mat.soft↗

arXiv2022

Statistical Mechanical theory for spatio-temporal evolution of Intra-tumor heterogeneity in cancers: Analysis of Multiregion sequencing data

Heterogeneity in characteristics from one region (sub-population) to another, commonly observed in complex systems, such as glasses and a collection of cells, is hard to describe theoretically. In the context of cancer, intra-tumor heterogeneity (ITH), characterized by cells with genetic and phenotypic variability that co-exist within a single tumor, is often the cause of ineffective therapy and recurrence of cancer. Multi-region sequencing (M-Seq), obtained by sampling multiple regions of a single tumor, has vividly demonstrated the pervasive nature of ITH, raising the need for a theory that accounts for evolution of tumor heterogeneity. Here, we develop a statistical mechanical theory to quantify ITH, using the Hamming distance, between genetic mutations in distinct regions within a single tumor. An analytic expression for ITH, expressed in terms of cell division probability ($\alpha$) and mutation probability ($p$), is validated using cellular-automaton type simulations. Application of the theory successfully captures ITH extracted from M-seq data in patients with exogenous cancers (melanoma and lung). The theory, based on punctuated evolution at the early stages of the tumor followed by neutral evolution, is accurate provided the spatial variation in the tumor mutation burden is not large. We show that there are substantial variations in ITH in distinct regions of a single solid tumor, which supports the notion that distinct subclones could co-exist. The simulations show that there are substantial variations in the sub-populations, with the ITH increasing as the distance between the regions increases. The analytical and simulation framework developed here could be used in the quantitative analyses of the experimental (M-Seq) data. More broadly, our theory is likely to be useful in analyzing dynamic heterogeneity in complex systems such as super-cooled liquids.

cond-mat.soft↗

arXiv2022

Tracer particles sense local stresses in an evolving multicellular spheroid without affecting the anomalous dynamics of the cancer cells

Measurements of local stresses on the cancer cells (CCs), inferred by embedding inert compressible tracer particles (TPs) in a growing multicellular spheroid (MCS), show that pressure decreases monotonically as the distance from the core of the MCS increases. How faithfully do the TPs report the local stresses in the CCs is an important question because pressure buildup in the MCS is dynamically generated due to CC division, which implies that the CC dynamics should be minimally altered by the TPs. Here using theory and simulations, we show that although the TP dynamics is unusual, exhibiting sub-diffusive behavior on times less than the CC division times and hyper-diffusive dynamics on in the long-time limit, they do not affect the long-time CC dynamics or the local CC stress distributions. The CC pressure profile within the MCS, which decays from a high value at the core to the periphery, is almost identical with and without the TPs. That the TPs have insignificant effect on the local stresses in the MCS implies that they are reliable reporters of the CC microenvironment.

cond-mat.soft↗

arXiv2022

Mechanical feedback controls the emergence of dynamical memory in growing tissue monolayers

The growth of a tissue, which depends on cell-cell interactions and biologically relevant process such as cell division and apoptosis, is regulated by a mechanical feedback mechanism. We account for these effects in a minimal two-dimensional model in order to investigate the consequences of mechanical feedback, which is controlled by a critical pressure, $p_c$. A cell can only grow and divide if the pressure it experiences, due to interaction with its neighbors, is less than $p_c$. Because temperature is an irrelevant variable in the model, the cell dynamics is driven by self-generated active forces (SGAFs) that are created by cell division. It is shown that even in the absence of intercellular interactions, cells undergo diffusive behavior. The SGAF driven diffusion is indistinguishable from the well-known dynamics of a free Brownian particle at a fixed finite temperature. When intercellular interactions are taken into account, we find persistent temporal correlations in the force-force autocorrelation function ($FAF$) that extends over timescale of several cell division times. The time-dependence of the $FAF$ reveals memory effects, which increases as pc increases. The observed non-Markovian effects emerge due to the interplay of cell division and mechanical feedback, and is inherently a non-equilibrium phenomenon.

cond-mat.soft↗

arXiv2021

Inter-particle adhesion regulates the surface roughness of growing dense three-dimensional active particle aggregates

Activity and self-generated motion are fundamental features observed in many living and non-living systems. Given that inter-particle adhesive forces are known to regulate particle dynamics, we investigate how adhesion strength controls the boundary growth and roughness in an active particle aggregate. Using particle based simulations incorporating both activity (birth, death and growth) and systematic physical interactions (elasticity and adhesion), we establish that inter-particle adhesion strength ($f^{ad}$) controls the surface roughness of a densely packed three-dimensional(3D) active particle aggregate expanding into a highly viscous medium. We discover that the surface roughness of a 3D active particle aggregate increases in proportion to the inter-particle adhesion strength, $f^{ad}$. We show that asymmetry in the radial and tangential active particle mean squared displacement (MSD) suppresses 3D surface roughness at lower adhesion strengths. By analyzing the statistical properties of particle displacements at the aggregate periphery, we determine that the 3D surface roughness is driven by the movement of active particle towards the core at high inter-particle adhesion strengths. Our results elucidate the physics controlling the expansion of adhesive 3D active particle collectives into a highly viscous medium, with implications into understanding stochastic interface growth in active matter systems characterized by self generated particle flux.

cond-mat.soft↗

arXiv2020

Self-generated persistent random forces drive phase separation in growing tumors

A single solid tumor, composed of nearly identical cells, exhibits heterogeneous dynamics. Cells dynamics in the core is glass-like whereas those in the periphery undergo diffusive or super-diffusive behavior. Quantification of heterogeneity using the mean square displacement or the self-intermediate scattering function, which involves averaging over the cell population, hides the complexity of the collective movement. Using the t-distributed stochastic neighbor embedding (t-SNE), a popular unsupervised machine learning dimensionality reduction technique, we show that the phase space structure of an evolving colony of cells, driven by cell division and apoptosis, partitions into nearly disjoint sets composed principally of core and periphery cells. The non-equilibrium phase separation is driven by the differences in the persistence of self-generated active forces induced by cell division. Extensive heterogeneity revealed by t-SNE paves way towards understanding the origins of intratumor heterogeneity using experimental imaging data.

physics.bio-ph↗

arXiv2020

Far from equilibrium dynamics of tracer particles embedded in a growing multicellular spheroid

By embedding inert tracer particles (TPs) in a growing multicellular spheroid the local stresses on the cancer cells (CCs) can be measured. In order for this technique to be effective the unknown effect of the dynamics of the TPs on the CCs has to be elucidated to ensure that the TPs do not greatly alter the local stresses on the CCs. We show, using theory and simulations, that the self-generated (active) forces arising from proliferation and apoptosis of the CCs drive the dynamics of the TPs far from equilibrium. On time scales less than the division times of the CCs, the TPs exhibit sub-diffusive dynamics (the mean square displacement, $\Delta_{TP}(t) \sim t^{\beta_{TP}}$ with $\beta_{TP}<1$), similar to glass-forming systems. Surprisingly, in the long-time limit, the motion of the TPs is hyper-diffusive ($\Delta_{TP}(t) \sim t^{\alpha_{TP}}$ with $\alpha_{TP}>2$) due to persistent directed motion for long times. In comparison, proliferation of the CCs randomizes their motion leading to superdiffusive behavior with $\alpha_{CC}$ exceeding unity. Most importantly, $\alpha_{CC}$ is not significantly affected by the TPs. Our predictions could be tested using \textit{in vitro} imaging methods where the motion of the TPs and the CCs can be tracked.

physics.bio-ph↗

arXiv2019

Spatially Heterogeneous Dynamics of Cells in a Growing Tumor Spheroid: Comparison Between Theory and Experiments

Collective cell movement, characterized by multiple cells that are in contact for substantial periods of time and undergo correlated motion, plays a central role in cancer and embryogenesis. Recent imaging experiments have provided time-dependent traces of individual cells, thus providing an unprecedented picture of tumor spheroid growth. By using simulations of a minimal cell model, we analyze the experimental data that map the movement of cells in fibrosarcoma tumor spheroid embedded in a collagen matrix. Both simulations and experiments show that cells in the core of the spheroid exhibit subdiffusive glassy dynamics (mean square displacement, $\Delta(t) \approx t^{\alpha}$ with $\alpha < 1$), whereas cells in the periphery exhibit superdiffusive motion, $\Delta(t) \approx t^{\alpha}$ with $\alpha>1)$. The motion of most of the cells near the periphery undergo highly persistent and correlated directional motion, thus explaining the observed superdiffusive behavior. The $\alpha$ values for cells in the core and periphery, extracted from simulations and experiments are in near quantitative agreement with each other, which is surprising given that no parameter in the model was used to fit the measurements. The qualitatively different dynamics of cells in the core and periphery is captured by the fourth order susceptibility, introduced to characterize metastable states in glass forming systems. Analyses of the velocity autocorrelation of individual cells show remarkable spatial heterogeneity with no two cells exhibiting similar behavior. The prediction that $\alpha$ should depend on the location of the cells in the tumor is amenable to experimental test. The highly heterogeneous dynamics of cells in the tumor spheroid provides a plausible mechanism for the origin of intratumor heterogeneity.

physics.bio-ph↗

arXiv2019

Dual Role of Cell-Cell Adhesion In Tumor Suppression and Proliferation Due to Collective Mechanosensing

It is known that mechanical interactions couple a cell to its neighbors, enabling a feedback loop to regulate tissue growth. However, the interplay between cell-cell adhesion strength, local cell density and force fluctuations in regulating cell proliferation is poorly understood. Here, we show that spatial variations in the tumor growth rates, which depend on the location of cells within tissue spheroids, are strongly influenced by cell-cell adhesion. As the strength of the cell-cell adhesion increases, intercellular pressure initially decreases, enabling dormant cells to more readily enter into a proliferative state. We identify an optimal cell-cell adhesion regime where pressure on a cell is a minimum, allowing for maximum proliferation. We use a theoretical model to validate this novel collective feedback mechanism coupling adhesion strength, local stress fluctuations and proliferation.Our results, predicting the existence of a non-monotonic proliferation behavior as a function of adhesion strength, are consistent with experimental results. Several experimental implications of the proposed role of cell-cell adhesion in proliferation are quantified, making our model predictions amenable to further experimental scrutiny. We show that the mechanism of contact inhibition of proliferation, based on a pressure-adhesion feedback loop, serves as a unifying mechanism to understand the role of cell-cell adhesion in proliferation.

cond-mat.soft↗