Neural Computation

Equilibrium propagation (EP) is a biologically plausible alternative to backpropagation that has demonstrated competitive performance across a range of machine learning tasks. Recent work has extended EP to spiking neural networks (SNNs), leveraging leaky integrate-and-fire (LIF) neurons and spike-based plasticity rules to improve biological realism while maintaining strong performance. In this work, we propose an EP-based SNN framework that combines LIF neural dynamics with a predictive learning rule, replacing conventional spike-timing-dependent plasticity (STDP) with a learning rule more directly aligned with predictive coding principles. We evaluate the proposed model on multiple image classification benchmarks, including MNIST, KMNIST, and Fashion-MNIST, and compare its performance with a BP-trained LIF SNN baseline. Our results show that the proposed EP-based LIF model (EP+LIF) achieves competitive accuracy across datasets, with performance approaching that of the BP-trained counterpart (BP+LIF) while relying on a biologically motivated local learning rule. In addition, analysis of hidden-layer spiking activity reveals that EP+LIF produces more persistent hidden-state activity, whereas BP+LIF yields sparser spiking representations. These results demonstrate that predictive learning can support effective EP-based training in LIF spiking networks, while also highlighting differences in activity patterns that motivate future work on activity regulation and sparse spiking dynamics.

The learning dynamics of biological brains and artificial neural networks are of interest to both neuroscience and machine learning. A key difference between them is that neural networks are often trained from a randomly initialized state whereas each brain is the product of generations of evolutionary optimization, yielding innate structures that enable few-shot learning and inbuilt reflexes. Artificial neural networks, by contrast, require non-ethological quantities of training data to attain comparable performance. To investigate the effect of evolutionary optimization on the learning dynamics of neural networks, we combined algorithms simulating natural selection and online learning to produce a method for evolutionarily conditioning artificial neural networks, and applied it to both reinforcement and supervised learning contexts. We found the evolutionary conditioning algorithm, by itself, performs comparably to an unoptimized baseline. However, evolutionarily conditioned networks show signs of unique and latent learning dynamics, and can be rapidly fine-tuned to optimal performance. These results suggest evolution constitutes an inductive bias that tunes neural systems to enable rapid learning.

Improving long-term memory in artificial neural networks remains an open challenge. To address this, we developed a novel brain-inspired framework for memory prioritization based on the principle of emotional valence. Our framework includes: (i) a valence-weighted cross-entropy loss that scales the learning signal by the valence magnitude, analogous to neuromodulation; (ii) an amygdala-inspired module that learns high-dimensional valence embeddings; and (iii) a hippocampus-inspired module that integrates valence embeddings into the attention mechanism to modulate information retrieval. We demonstrated the generalization of our framework across spatial, episodic, and language-based memory tasks, consistently improving memory prioritization and long-term retention of high-salience information. In addition to improving long-term memory, we also showed that our framework can help mitigate the "lost-in-the-middle" problem in language modeling. More generally, this research provides further evidence of the potential of brain-inspired algorithms to advance the field of machine learning.

The routing of information across the brains structural network is central to its wide range of functional capabilities. However, the mechanisms underlying information routing in complex brain networks, particularly between regions that do not share a direct anatomical connection, remain poorly understood. Neural mass models (NMMs), a computational modelling framework capable of capturing complex neural dynamics across scales, can potentially be used to study the dynamical and network bases of these vital polysynaptic routing processes. In this study, we investigate polysynaptic signalling in three widely used NMMs, obeying Ornstein-Uhlenbeck, Stuart-Landau, and Jansen-Rit dynamics, by tracking the propagation of a discrete, focal, high-amplitude perturbation across the underlying network. We find that polysynaptic propagation emerges in all tested NMMs when configured within dynamical regimes that effectively enhance the persistence of perturbations. We also find distinct parameter domains that maximise signal propagation to directly connected regions and to those separated from the source by at least two hops. Finally, we benchmark in silico stimulus propagation in the brain network against an empirical dataset of direct electrical stimulation trials, to explore the relative capabilities of the NMMs in capturing signal propagation to connected versus unconnected regions. This analysis highlights the significance of dynamical repertoire in capturing stimulus propagation outcomes. Overall, this study provides insights into how dynamical and network features shape signal propagation over complex brain networks.

Scientific models are widely used across the natural sciences as an interface between scientific theories and empirical data [1]. Such models play a key role, for example, in the study of human and animal learning, where they express algorithmic hypotheses and relate them to psychology and neuroscience data [2, 3]. These models are traditionally handcrafted by expert researchers based on existing theory or new insights. Such handcrafted models, however, are now known to fall short of capturing the full richness of behavior, even in their narrow domains [4-7]. An alternative data-driven approach has emerged, seeking to discover new insights by fitting and interpreting flexible models [8-11]. However, these tools require substantial human effort to derive insight from data, and it has been unclear how to discover new ideas from data efficiently. Here, we present DataDIVER, a general approach for automatically discovering computational models from data, and demonstrate that these models surface novel mechanistic insights into human and animal learning. Our approach delivers models that take the form of short computer programs, which are optimized both to fit data well and to be simple. These programs explicitly connect with existing theoretical frameworks and are readily understandable by human scientists. They can also be used to make novel predictions, some of which we show are borne out in re-analysis of existing data. General-purpose tools for surfacing new ideas from data, especially in combination with the large datasets that are increasingly available in many fields, stand to dramatically accelerate scientific discovery.

The awake brain is known to display asynchronous (AS) states during periods of attention and arousal, but the responsiveness properties of such states remain unclear. Here, we investigate this question using computational models of spiking networks of excitatory and inhibitory neurons, mimicking recurrently-connected networks in layer 2/3 of the cerebral cortex. The networks can generate a continuum of AS states, but with different responsiveness characteristics. By using a mean-field model to infer the dynamic properties of the system, we find that there are two families of AS states, which we call "underdamped" (UD) and "overdamped" (OD). Responsiveness is maximised at the transition between OD and UD states, which identifies a "working point" that may present advantageous computational properties.

Rhythm is a key building block of human music, speech and numerous other human activities. Understanding the computational substrates of rhythm perception requires models that bridge algorithmic function with biological implementation. We propose a physiologically grounded spiking neural network (SNN) framework to investigate the emergent representation and interpretation of auditory rhythms. Utilizing a recurrent SNN architecture trained on an auditory entrainment task, we characterize the networks latent dynamics through the analysis of firing rates and membrane potential fluctuations. Our results demonstrate that simulated neural populations exhibit phase-locking to the stimulus beat, with endogenous oscillations driven by rhythmic input. We further show that anticipatory dynamics--characterized by pre-stimulus depolarization--emerge naturally from the networks synaptic plasticity and temporal integration properties, rather than from explicitly defined oscillators. By treating network layers as functional analogs of cortical populations, this framework allows for the application of spectral and information-theoretic analyses typical of empirical electrophysiology. More in general, this approach establishes SNNs as robust exploratory tools for uncovering how predictive coding and rhythmic entrainment arise from the inherent constraints of biological neural computation.

IntroductionAlthough neural activity is organized across temporal and spatial scales, the principles that determine the accuracy and fidelity of neural information representation across scales remain unclear. In particular, while recent empirical results have reported mesoscopic optimality in neural decoding, no theoretical accounts exist that explain when and why such intermediate scales emerge as optimal. Here, we develop an analytical framework to study the optimal temporal scale of information representation and its dependence on the dynamic structure of signal and noise in neural data. Materials and MethodsWe formulate a multiscale theoretical model in which neural population activity is represented by temporally encoded trial vectors at microscopic, mesoscopic, and macroscopic resolutions. Neural responses are modeled as class-dependent mean activations (signal) corrupted by temporally correlated noise, and decay rates of correlations in both signal and noise are varied parametrically. Representational quality at each scale is quantified using the sensitivity index (d-prime) for decoding condition from neural activity. ResultsWe derive closed-form expressions for the sensitivity index at each temporal scale. These expressions reveal the key roles of signal and noise correlations as the main determinants of condition decodability at all scales. Comparing expressions under various combinations of signal and noise correlations reveals two regimes. First, when signal and noise correlations are absent or persistent over time, the optimal resolution falls at one of two extremes: macroscale (resp. microscale) if signal correlations are stronger (resp. weaker) than noise correlations. In contrast, when both signal and noise correlations decay with temporal separation, temporal integration produces a nontrivial trade-off: moderate integration improves decodability by suppressing noise while preserving coherent signal, whereas excessive integration degrades signal and decodability. Therefore, only in the latter regime, mesoscopic representations emerge as optimal across a broad range of biologically plausible parameters. DiscussionThis work provides a theoretical explanation for how the optimal temporal scale of neural information representation depends on the interplay between signal and noise correlations and their temporal decay. Broadly, the framework establishes temporal integration as a principled mechanism linking multiscale neural dynamics to information representation and offers testable predictions across recording modalities and neural systems.

Categorisation is often treated as a form of compression: a high-dimensional stimulus space is reduced to a smaller set of behaviourally or cognitively useful classes. However, compression alone does not determine whether a category map is useful. The present manuscript develops an information-theoretic framework for evaluating categorisation in terms of both category complexity and target-relevant information preservation. Across a set of synthetic demonstrations, alternative category maps over the same stimulus space are shown to preserve different target variables, including identity, action, nuisance, and hierarchical category structure. The framework is then extended to learned visual representations by analysing layer-derived category maps from a pretrained ResNet-50 network applied to CIFAR-10 images. Two scenarios are compared: a clean-only object run and a pooled nuisance run containing clean, blurred, pixelated, and noise-perturbed images. The results show that category maps can have substantial entropy while preserving information about a variable that is not aligned with the specified target, and that the value of a categorisation depends on the target variable to be preserved. The manuscript argues that categorisation should therefore be evaluated not only by compression or separability, but by the information retained about a specified cognitive, behavioural, or computational target.

Understanding how neuronal populations interact to encode and transform sensory information is a fundamental challenge in computational neuroscience. Most existing studies, however, study neural encoding, behavioral readout, and functional connectivity as disjoint problems. Two-photon calcium imaging enables simultaneous recording of large neuronal ensembles in vivo, driven by diverse stimuli and eliciting distinct behaviors. However, extracting directional functional connectivity metrics as well as encoding and readout properties of neurons from such data remains difficult due to indirect and noisy observations of spiking activity, slow temporal dynamics, and the latent interplay between external stimuli and endogenous neural processes. Here, we introduce a unified conceptual and operational modeling and inference framework for directly extracting functional Granger causal (GC) effects between neurons, from external stimuli to neurons, and from neurons to behavior, from two-photon imaging data, in the sense of Granger. Inspired by the intersection information framework, we also identify neurons that encode features of sensory stimuli that inform behavioral readout. The resulting GC networks together with the taxonomy of functional sensori-behavioral relevance, which we call G-taxonomy, provides a powerful statistical analysis framework, enabled by the integration of several techniques including state-space modeling and inference, variational inference, and point processes. We applied the proposed framework to simulated and experimentally-recorded two-photon imaging from the mouse auditory cortex (A1) during both passive listening and active tone discrimination. Our simulation studies reveal significant improvement of our proposed methodology over existing techniques. Analysis of experimental data from the mouse A1 identifies distinct groups of cells with diverse sensori-behavioral relevance, as well as changes in functional connectivity associated with correct vs. incorrect behavior. In summary, this work provides a principled and data-driven methodology for uncovering directional interactions among the neurons, sensory stimuli, and behavior, all within the same statistical framework, offering new insights into how distributed cortical populations transform sensory inputs into behaviorally relevant representations. Author SummaryThe brain processes sensory inputs through the coordinated activity of large networks of neurons and produces readouts that elicit behavior. Understanding how information flows and is processed through these networks is a central goal of neuroscience. In this study, we present a new computational framework that identifies directional interactions among neurons in an ensemble as well as from sensory stimuli to neurons and from neurons to behavior. Utilizing the Granger formalism to identify directional effects, as opposed to common correlational measures, our framework extracts said effects directly from two-photon calcium imaging data. We tested our proposed method on both simulated data and recordings from the auditory cortex of mice during passive listening and active tone discrimination tasks. Our method revealed diverse groups of neurons in the auditory cortex with distinct functional roles and relevance to sensori-behavioral integration. Our framework provides a new way to study the flow of information in the brain and can be broadly applied to uncover neural computations across sensory and cognitive systems.

Population analysis methods have become standard for navigating the complexity of neural data. However, these methods often assume a rate code, neglecting information encoded in the precise timing of spikes. Critically, additional information encoded in bursts of action potentials may be missed. Here, we develop a factor analysis method that disentangles the factors associated with bursts and individual spikes. This enables burst codes to be investigated directly from the structure of the data, without requiring external covariates. We demonstrate that analyzing firing rates alone obscures the latent structure and factors underlying bursts. Applying our method to simulated and experimental data, we show that it can infer the correct latent structure and be used to test for the presence of burst coding. By merging the population and burst coding perspectives, we provide a framework for linking changes in bursting to internal variables involved in attention, perception, and learning.

The ability of the brain to encode information and control behavior depends on the coordinated activity of large and distributed neuronal populations. Correlations in neuronal spiking activity across trials of the same condition, or noise correlations (NCs), have been interpreted as a reflection of shared synaptic connectivity and as a contributing factor to the information capacity of neuronal populations. The impact of NCs on coding is most often considered in populations of neurons exhibiting robust condition-dependent information in their spike counts (SCs). However, theoretical work suggests that NCs could provide a source of condition-dependent information separate from SCs. We examined the activity of large neuronal populations in prefrontal cortex of macaques while they performed a spatial delayed response task composed of visual, memory, and motor epochs. We found that pairs of neurons that displayed visual, memory, and motor selectivity in their SCs often exhibited selectivity in their NCs, independent of spike count. However, we also found that pairs of neurons without SC selectivity during the different task epochs nonetheless exhibited condition-dependent NCs. Moreover, we found that the magnitude of condition-dependent NCs were largely comparable across neuronal pairs with or without SC selectivity. These results demonstrate that correlated variability in spiking activity can be condition-dependent even in the absence of condition-dependent SCs.

Humans frequently make decisions in complex, high-dimensional environments, where identifying task-relevant information is critical for rapid behavior optimization. Humans outperform standard reinforcement learning agents in navigating such complexity, yet the cognitive strategies of humans remain unclear. To address this, we developed a novel multi-dimensional learning task in which only a subset of dimensions is reward-related. Crucially, unlike prior studies, subjects are uninformed of the true task dimensionality and have to identify them through exploration. This design closely mimics the ambiguity in real-world tasks. Our results have identified two stereotyped choice patterns that reveal "dimension-guided" strategies in exploration and exploitation. Cross-subject analyses suggest that dimension-guided exploration may promote the efficiency of reward-based learning. These findings indicate that humans leverage task dimensionality to guide exploration, and provide inspiration for improving exploration efficiency in AI agents.

Growing interest to describe the electrical behavior of glial cells, mainly astrocytes, in intact brain tissue poses more and more challenges to commonly accepted belief they only respond in a linear manner in uptake of the excess of extracellular potassium and maintenance of their network equipotentiality. Their highly conductive mutual interconnections via gap junction (GJ) connections introduce yet another class of nonlinear elements. As more studies report nonlinearities in membrane voltage Vm dependence of both, the membrane and junctional conductances, the need to formulate minimal dynamical models of their transient behavior is getting more acute. Since ODE models of coupled cells, even in simplest 1-d arrays, require simplified descriptions and small set of parameters, rare quantitative studies on glia makes the task even more difficult. This study attempts to qualify a self-coupled cell, or a glial cell coupled to fixed voltage as useful system for detecting the nature of instabilities and transitions coming from coupling. In a novel biophysical model of coupled astrocyte, we introduce nonlinear kinetics of deactivation for large junctional voltages for the first time. We found that N-shaped nonlinearities and corresponding fold structure in the vector field of isolated cell serves as a baseline on top of which coupling nonlinearities enrich the bifurcation picture. Numerical simulations of 1-d array of coupled astrocytes show that coupling increases the propensity of astrocytic Vm to bistability and front propagation. We believe that presented illustrations of possible effects of coupling nonlinearities will motivate neurobiologists to further explore their impact in disease. Significance statementTransient changes in membrane voltage of glial cells may produce significant transient voltage difference between directly coupled cells. Nonlinear steady-state conductance of their interconnection elements, the gap junctions, introduce nonlinear current profiles which are very difficult to measure and quantitate using the available methods due to marked permeability of the junctions and leakiness of glial membrane in general. We propose a minimal model of glial membrane extended with a self-coupled feedback loop, which under realistic simplifying assumptions could serve for qualitative analysis of the impact of coupling, on the stability of resting membrane voltage. Neuronal cells of the brain and spinal cord cannot exist and function without supportive and neuromodulatory functions of the diverse population of glial cells. This applies to virtually all physiological processes on cell level - from cell development, metabolic support, membrane signaling, slow molecular signal transduction, ion homeostasis, neurovascular coupling, myelination, to mention only a few, manifest neuro-glial interaction. Even though all glial cell types are interconnected, the most abundant ones, the astrocytes are massively interconnected by gap junctions to form ordered networks. Electrically, astrocytic networks display membrane voltage equipotentiality, which is considered system-wide resting state for given neuro-glial circuit or unit. With molecular and cellular substrates of glial connectivity being slowly elucidated, network science and dynamical modeling are slowly "invading" that area with many important issues left open. In this study using classical dynamical systems approaches we give indications how nonlinear intercellular coupling between astrocytes affects physiological resting state and its instabilities compared to isolated, uncoupled cell. We strongly believe the suggested minimal model could fill the gap in ODE modeling of neuro-glial circuits, within broadest scope of hypothesis-driven research in cell-level neuroscience.

In contrast to static formalisms, computational definitions describe the operational mechanisms of a model. Simulations are an essential part of the cycle of theory development and refinement, assisting researchers in formulating the precise definitions that models require, and making accurate predictions. This manuscript introduces a computational implementation of Pavlovian learning models in a Python environment, termed Pavlovian Associative Learning Models Simulation (PALMS). In addition to the canonical Rescorla-Wagner model, attentional approaches are implemented, including Pearce-Kaye-Hall, Mackintosh Extended, Le Pelleys Hybrid, and a novel extension of the Rescorla-Wagner model featuring a unified variable learning rate that synthesises Mackintoshs and Pearce and Halls opposing conceptualisations. To our knowledge, only the first attentional model has been previously specified computationally in a general design tool. PALMS integrates a graphical interface that permits the input of entire experimental designs in an alphanumeric format, akin to that used by experimental neuroscientists. It uniquely enables the simulation of experiments involving hundreds of stimuli, such as those used with human participants, and the computation of configural cues and configural-cue compounds across all models, thereby substantially broadening their predictive capabilities. A comprehensive description of the models implementation and the environment functionalities is provided in the paper; these include efficient and accurate operation and instant visualisation of predicted results across different models within a single architecture and environment. We evaluate PALMS by simulating five published experiments in the associative learning literature that assessed the predictive scope of existing models, and we show that this implementation provides neuroscientists with a useful tool for identifying critical variables, refining experimental designs, making precise predictions, comparing model fitness, and formulating new theoretical approaches. PALMS is licensed under the open-source GNU Lesser General Public License 3.0. The environment source code and the latest multiplatform release build are accessible as a GitHub repository at https://github.com/cal-r/PALMS-Simulator. Author summaryResearch on associative learning is multidisciplinary, encompassing disciplines such as neuroscience, AI, psychology, psychiatry, behavioural sciences, planning, and marketing. Unlike static formalisms, precise computational definitions specify how a model operates, enabling model simulation, swift and error-free prediction calculations, which are essential for testing theories, comparing predictions, holding models accountable, and providing a common language across fields. We introduce Pavlovian Associative Learning Models Simulation (PALMS), a user-friendly, open-source Python environment for simulating classical conditioning and studying the role of attention in learning. PALMS implements the prescriptive Rescorla-Wagner and attentional models: Pearce-Kaye-Hall, Mackintosh Extended, Le Pelleys Hybrid, and a new hybrid model with a unified variable learning rate that blends Mackintosh and Pearce-Halls conflicting views. Its graphical interface makes it easy for neuroscientists to enter experiments. Our computational implementation supports simulations with hundreds of stimuli, configural cues, and compounds, broadening the models predictive power. Designed for efficiency, it offers instant visual results and useful features. We evaluate PALMS by simulating five published experiments, highlighting its value for model comparison and refinement, and, more generally, as a tool to assist research.

Human goal pursuit is often marked by persistent activity toward achieving an objective, as well as flexibility in switching objectives based on environmental demands. How humans balance the stability and flexibility necessary for goal pursuit is the key question of this study. We propose that goal pursuit generates dynamic attractor modes in policy landscapes that produce stability in goal pursuit. The attractor properties are modulated through progress monitoring, allowing for the flexibility necessary to switch objectives in favor of alternative goals. Through simulations and behavioral cloning of human participants performing an extended goal selection task, we show how dynamic modes can develop in the latent spaces of recurrent neural networks trained with reinforcement learning. We develop metrics to quantitatively assess the attractor qualities of dynamic modes, validating them against synthetically generated dynamical systems, and use them to investigate the context modulation of attractor modes during goal pursuit. We then proceed to develop a circuit-level account of goal persistence incorporating self-excitation and cross-inhibition as motifs for fast, self-sustaining dynamics modulated by slow, progress-integrating momentum and context signals. Lastly, we show that the switching costs experienced while managing multiple goals are an emergent property of resistance to the intrinsic dynamics of goal pursuit, thereby contributing a fresh perspective on the dynamics of extended goal pursuit.

Perceptual systems in humans and many other animals are able to segment scenes into regions that are likely to be physically meaningful. This ability depends on having low-level mechanisms that can accurately categorize whether local image patches are samples from the same or different kinds of texture. We find that using spatial proximity as a proxy for same-different ground truth makes it possible to train accurate decision variables and bounds directly from arbitrary natural images with no feedback. We also find that performance can be further improved by using proximity as a ground truth for adjusting the final decision variables and bounds for the current image/scene. These surprising findings result from the simple fact that under a wide range of conditions proximity discrimination (near vs. far) and texture discrimination (same vs. different) have mathematically identical decision bounds if the same image features are used for both tasks. We used the decision variables and bounds trained on natural images as the initial steps in a hierarchical Bayesian observer (HBO) model of texture discrimination [9]. Given the relative simplicity of this HBO model, it did an excellent job of segmenting images having randomly shaped regions containing arbitrary natural textures. We suggest that the proximity proxy is something that natural selection could discover and exploit for any same-different task where the task-relevant stimulus features also vary systematically with distance in space and/or time. For example, natural selection could have created developmental learning/plasticity mechanisms that exploit the proximity proxy.

Cerebellar neural circuit dynamics rely on a rich repertoire of synaptic and excitability mechanisms, which are thought to determine network computation in physiological and pathological conditions. In this work, we develop and validate a biologically-grounded spiking neural network of the cerebellar cortex, embedding key mechanisms of cellular excitability and synaptic transmission, and assess their impact on signal processing. Neuronal input-output functions, short-term synaptic plasticity, receptor-specific kinetics, and NMDA channel voltage-dependent gating were calibrated against detailed multicompartmental models through automatic tuning procedures. Incorporating these realistic biological properties allowed the network model to simulate key features observed in recordings from acute cerebellar slices. The neuronal discharge and local field potentials elicited by mossy fiber stimulation faithfully reproduced the natural patterns with millisecond precision. Then, selective receptor switch-off revealed the contribution of NMDA, GABA, and AMPA receptors to the frequency-dependent input-output function of the granular layer and Purkinje cells, linking previous empirical findings to specific synaptic mechanisms. This model combines high computational performance with biological realism and offers a computationally efficient framework to investigate neurophysiological phenomena and the neural correlates of behavior in large-scale long-lasting simulations, such as those needed to address the neural underpinnings of learning and of cerebellar pathologies.

Adolescence is an important developmental period during which there are diverse changes in the brain and behavior. Goal-directed behaviors and the component processes underlying those behaviors improve during adolescence, including working memory, response inhibition, and reinforcement learning. At the same time there is substantial pruning of excitatory connections in prefrontal cortex and ongoing myelination of axons. However, psychiatric disorders also become increasingly prevalent in late adolescence and early adulthood. In this study, we develop computational models that suggest a hypothesis for how the ongoing changes in the brain can give rise to the increased prevalence of psychiatric disorders. We show that both myelination and pruning during adolescence lead to attractor landscapes in which strongly encoded memories, driven by three-factor learning rules that modulate Hebbian plasticity, come to dominate the landscape of brain activity, at the expense of weakly encoded memories. Pruning and myelination lead to large, strong attractors which, if they are related to aversive emotions, can drive intrusive thoughts and compulsions in obsessive compulsive disorder, rumination in depression, and aversive memories in post-traumatic stress disorder. The link between pruning, myelination and the emergence of dominant attractors for emotionally salient memories is well supported by the models. The way these effects map onto forebrain circuits requires more work.

Parameter estimation in nonlinear biological dynamical systems is a difficult inverse problem because the governing equations are often stiff or oscillatory, the data are sparse and noisy, and the objective landscape is non-convex. Physics-informed neural networks (PINNs) offer an alternative to purely simulation-based calibration by representing state trajectories with neural networks while penalizing violations of the governing equations. This paper studies the empirical reliability of PINNs for recovering the parameters of the repressilator, a synthetic genetic oscillator formed by three cyclically repressive genes. We use synthetic time-series generated from the standard ordinary differential equation model and train inverse PINNs to estimate the production parameter {beta} and the Hill coefficient n. The study varies observation noise, partial observation of repressors, sampling density, sensitivity to initial parameter guesses, and the difference between stable and oscillatory regimes. The results show that PINNs can reconstruct trajectories accurately when the model structure is correct and the three repressors are observed, but parameter recovery is more fragile than trajectory fitting. Noise, sparse sampling, unobserved variables, and unfavorable initial guesses increase the risk of biased estimates. The stable regime is easier to reconstruct, whereas the oscillatory regime provides richer information but also exposes optimization sensitivity. These findings support PINNs as a useful reverse-engineering tool for small gene-regulatory ODE models, while highlighting the need for repeated runs, uncertainty reporting, and experimental designs that improve identifiability.