Neural boundary shape functions in physics-informed neural networks for discontinuous and high-frequency problems

A major challenge in neuroscience is to determine the rules that govern the structural and functional interdependence of cellular neural circuits and networks in the brain [1]. This challenge is a difficult one given the fact that brain networks are complex networks with emergent behaviors and properties. Understanding the underlying mechanisms that shape the intimate relationship between structure and function will help us better understand how functional brain states emerge from their underlying structural substrate, in addition to providing us with new insights into how the disruption of this function-structure interdependence will affect brain function. It is clear that structure and function are interrelated and that specific brain regions and even specific brain networks have well defined structural topologies, determined by the very specific neuron types that they recruit and the specific connections that these neurons project [2]. This fundamental property plays a major role in determining functions that are characteristic of certain brain networks. However, it is less clear how experience and exposure to external cues can lead to the emergence of fast and flexibly reconfigured functional networks that are bound by a well defined structural substrate, and how this structural substrate in turn, but at a slower time scale, may reshape functional networks. Even more intriguing is the fact that such functional networks, while highly dynamic, play a major role in remodeling, associating and storing information that is presented by external cues for time periods that can sometimes extend over an individual’s lifetime; in short they underlie learning and memory. Despite considerable advances in experimental techniques and computational paradigms, our understanding of this problem is still incomplete. We have begun to address this issue by developing a model that is composed of integrate-and-fire excitatory and inhibitory neurons that are connected to external inputs and project recurrent connections among themselves. It is based on the hypothesis that functional network dynamics are bound by three main rules: (1) Structural network connectivity is predetermined to a high extent and is a prerequisite for functional connectivity to take place between two neurons. (2) Synaptic plasticity that the network undergoes is Hebbian-like and weight change (following potentiation or depression) is proportional to the number of afferents of a certain neuron. (3) Heterosynaptic plasticity takes place to help regulate the neuronal firing rate. Our results show that structure and synaptic plasticity determine function at large and sets boundaries to the information capacity of the neuronal network. We also tested different network sizes and different physical connectivity constraints in order to determine how the emergent functional dynamics and network capacity scale with the network size. Here we present and discuss our data and results to date with this model. We aim, through this theoretical study and in the long run, to come full circle to a better and more integrated understanding of the intricate interdependence between structure and function in brain networks as shaped by learning and memory. Unraveling these dynamics will directly contribute to our understanding of how different parts of the mammalian brain function in health, how they fail in disease, and how best to guide nervous system related therapies.

Epilepsy surgery outcome and functional network alterations in longitudinal MEG: A minimum spanning tree analysis

Discretization-based methods like the finite element method have proven to be effective for solving the Helmholtz equation in computational acoustics. However, it is very challenging to incorporate measured data into the model or infer model input parameters based on observed response data. Machine learning approaches have shown promising potential in data-driven modeling. In practical applications, purely supervised approaches suffer from poor generalization and physical interpretability. Physics-informed neural networks (PINNs) incorporate prior knowledge of the underlying partial differential equation by including the residual into the loss function of an artificial neural network. Training the neural network minimizes the residual of both the differential equation and the boundary conditions and learns a solution that satisfies the corresponding boundary value problem. In this contribution, PINNs are applied to solve the Helmholtz equation within a two-dimensional acoustic duct and mixed boundary conditions are considered. The results show that PINNs are able to solve the Helmholtz equation very accurately and provide a promising data-driven method for physics-based surrogate modeling.

Professional musicians are a popular model for investigating experience-dependent plasticity in human large-scale brain networks. A minority of musicians possess absolute pitch, the ability to name a tone without reference. The study of absolute pitch musicians provides insights into how a very specific talent is reflected in brain networks. Previous studies of the effects of musicianship and absolute pitch on large-scale brain networks have yielded highly heterogeneous findings regarding the localization and direction of the effects. This heterogeneity was likely influenced by small samples and vastly different methodological approaches. Here, we conducted a comprehensive multimodal assessment of effects of musicianship and absolute pitch on intrinsic functional and structural connectivity using a variety of commonly used and state-of-the-art multivariate methods in the largest sample to date (n = 153 female and male human participants; 52 absolute pitch musicians, 51 non-absolute pitch musicians, and 50 non-musicians). Our results show robust effects of musicianship in interhemispheric and intrahemispheric connectivity in both structural and functional networks. Crucially, most of the effects were replicable in both musicians with and without absolute pitch compared with non-musicians. However, we did not find evidence for an effect of absolute pitch on intrinsic functional or structural connectivity in our data: The two musician groups showed strikingly similar networks across all analyses. Our results suggest that long-term musical training is associated with robust changes in large-scale brain networks. The effects of absolute pitch on neural networks might be subtle, requiring very large samples or task-based experiments to be detected.SIGNIFICANCE STATEMENT A question that has fascinated neuroscientists, psychologists, and musicologists for a long time is how musicianship and absolute pitch, the rare talent to name a tone without reference, are reflected in large-scale networks of the human brain. Much is still unknown as previous studies have reported widely inconsistent results based on small samples. Here, we investigate the largest sample of musicians and non-musicians to date (n = 153) using a multitude of established and novel analysis methods. Results provide evidence for robust effects of musicianship on functional and structural networks that were replicable in two separate groups of musicians and independent of absolute pitch ability.

SummaryDefining the rules governing synaptic connectivity is key to formulating theories of neural circuit function. Interneurons can be connected by both electrical and chemical synapses, but the organization and interaction of these two complementary microcircuits is unknown. By recording from multiple molecular layer interneurons in the cerebellar cortex, we reveal specific, nonrandom connectivity patterns in both GABAergic chemical and electrical interneuron networks. Both networks contain clustered motifs and show specific overlap between them. Chemical connections exhibit a preference for transitive patterns, such as feedforward triplet motifs. This structured connectivity is supported by a characteristic spatial organization: transitivity of chemical connectivity is directed vertically in the sagittal plane, and electrical synapses appear strictly confined to the sagittal plane. The specific, highly structured connectivity rules suggest that these motifs are essential for the function of the cerebellar network.

A digital twin (DT) for nuclear reactor monitoring can be implemented using either a differential equations-based physics model or a data-driven machine learning model. The challenge of a physics-model-based DT consists of achieving sufficient model fidelity to represent a complex experimental system, whereas the challenge of a data-driven DT consists of extensive training requirements and a potential lack of predictive ability. We investigate the performance of a hybrid approach, which is based on physics-informed neural networks (PINNs) that encode fundamental physical laws into the loss function of the neural network. We develop a PINN model to solve the point kinetic equations (PKEs), which are time-dependent, stiff, nonlinear, ordinary differential equations that constitute a nuclear reactor reduced-order model under the approximation of ignoring spatial dependence of the neutron flux. The PINN model solution of PKEs is developed to monitor the start-up transient of Purdue University Reactor Number One (PUR-1) using experimental parameters for the reactivity feedback schedule and the neutron source. The results demonstrate strong agreement between the PINN solution and finite difference numerical solution of PKEs. We investigate PINNs performance in both data interpolation and extrapolation. For the test cases considered, the extrapolation errors are comparable to those of interpolation predictions. Extrapolation accuracy decreases with increasing time interval.

In recurrent neural networks such as the long short-term memory (LSTM), the sigmoid and hyperbolic tangent functions are commonly used as activation functions in the network units. Other activation functions developed for the neural networks are not thoroughly analyzed in LSTMs. While many researchers have adopted LSTM networks for classification tasks, no comprehensive study is available on the choice of activation functions for the gates in these networks. In this paper, we compare 23 different kinds of activation functions in a basic LSTM network with a single hidden layer. Performance of different activation functions and different number of LSTM blocks in the hidden layer are analyzed for classification of records in the IMDB, Movie Review, and MNIST data sets. The quantitative results on all data sets demonstrate that the least average error is achieved with the Elliott activation function and its modifications. Specifically, this family of functions exhibits better results than the sigmoid activation function which is popular in LSTM networks.

BackgroundThree intrinsic connectivity networks in the brain, namely the central executive, salience, and default mode networks, have been identified as crucial to the understanding of higher cognitive functioning, and the functioning of these networks has been suggested to be impaired in psychopathology, including posttraumatic stress disorder (PTSD).Objective1) To describe three main large-scale networks of the human brain; 2) to discuss the functioning of these neural networks in PTSD and related symptoms; and 3) to offer hypotheses for neuroscientifically-informed interventions based on treating the abnormalities observed in these neural networks in PTSD and related disorders.MethodLiterature relevant to this commentary was reviewed.ResultsIncreasing evidence for altered functioning of the central executive, salience, and default mode networks in PTSD has been demonstrated. We suggest that each network is associated with specific clinical symptoms observed in PTSD, including cognitive dysfunction (central executive network), increased and decreased arousal/interoception (salience network), and an altered sense of self (default mode network). Specific testable neuroscientifically-informed treatments aimed to restore each of these neural networks and related clinical dysfunction are proposed.ConclusionsNeuroscientifically-informed treatment interventions will be essential to future research agendas aimed at targeting specific PTSD and related symptoms.

White matter hyperintensities (WMH) are clinical markers of subcortical ischemic vascular cognitive impairment (SIVCI) associated with impaired postural balance and falls. Physical reserve (PR) is a recently established construct that reflects one’s capacity to maintain physical function despite brain pathology. This cross-sectional study aims to map functional networks associated with PR, and examining the relationship between PR, WMH, and postural balance. Physical reserve was defined in 22 community-dwelling older adults with SIVCI as the unexplained residual variance in Timed-Up-and-Go test (TUG) after accounting for age, global cognitive function measured by Alzheimer’s Disease Assessment Scale-Cognitive-13 (ADAS-Cog-13), and hippocampal volume. Functional neural networks associated with PR were extrapolated as TUG-correlated network connectivity maps computed using general linear models that removed the effects of age, ADAS-Cog-13, and hippocampus volume. Subsequent analyses examined whether PR and its associated brain networks moderated the relationship between WMH and postural balance under two conditions – eyes open while standing on foam (EOF) and eyes open while standing on floor (EONF). Physical reserve and its associated functional neural networks - frontoparietal network (FPN) and default mode network (DMN) - significantly moderated the association between WMH and postural balance. Specifically, in those with high PR, postural balance was maintained regardless of WMH load while in those with low PR, postural balance worsened as WMH load increased. These results suggest the attenuated effects of WMH on postural stability due to PR may be underpinned by functional neural network reorganization in the FPN and DMN as a part of compensatory processes.

Models of spiking neural networks have a great potential to become a crucial tool in the development of complex network theory. Of particular interest, these models can be used to better understand the important class of brain functional networks, which are frequently studied in the context of computational network analysis. A fundamental question is whether functional connectivity sampling via surface multichannel recordings is able to reproduce the main connectivity features of the underlying spatial neural network. In this work we address this problem through computational modeling using the integrate-and-fire spiking neuron model, which enabled us to relate neural connectivity and the respective mesoscopic dynamics. Functional samples were then compared to an idealized spatial neural network model in terms of established topological network measurements. Results show that some measurements (e.g., betweenness centrality) are able to fairly approximate functional and spatial networks. Therefore, under specific circumstances of sampling size and simulation approach, it is possible to say that functional networks are able to reproduce connectivity features of the underlying neural network.

Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for solving high-dimensional partial differential equations and have demonstrated promising results across various fields of physics and engineering. In this paper, we present the first application of PINNs to quantum tunneling in heavy-ion fusion reactions. By incorporating the physical laws directly into the neural network's loss function, PINNs enable the accurate solution of the multidimensional Schrödinger equation, whose wavefunction has substantial oscillations. The calculated quantum tunneling probabilities exhibit good agreement with those obtained using the finite element method at the considered near barrier energy region. Furthermore, we demonstrate a significant advantage of the PINN approach to save and fine-tune pre-trained neural networks for related tunneling calculations, thereby enhancing computational efficiency and adaptability.

In recent years, Physics-Informed Neural Networks (PINNs) have introduced a novel approach to solving partial differential equations (PDEs) using deep learning techniques. Despite the promising results and rapid advancements in the field, there is a lack of more accurate studies concerning properties related to modeling choices within the deep learning framework, especially, but not exclusively, in solid mechanics problems. In this study, we aim to explore whether the neural network architecture, activation function, optimizer, and sampling method can influence the accuracy of results and training speed for solid mechanics problems. We will focus on elasticity and hyperelasticity problems in 1D, 2D, and 3D dimensions to lay the groundwork for more complex investigations.

MFLP-PINN: A physics-informed neural network for multiaxial fatigue life prediction

This research mainly based on multilayer perceptron (MLP) neural networks technique of data mining to forecast the wheat crop yield at the district level. There are many statistical and simulation models available, but the proposed algorithm with new activation function provides promising results in a shorter time with more accuracy. Sigmoid and hyperbolic tangent activation functions are widely used in the neural network. The activation functions play an important role in the neural network learning algorithm. The main objective of the proposed work is to develop an amended MLP neural network with new activation function and revised random weights and bias values for crop yield estimation by using the different weather parameter datasets. MLP model has been tested by existing activation functions and newly created activation functions with different cases including weights and bias values. In this research study, we evaluate the result of different activation functions and recommend some new simple activation functions, named DharaSig, DharaSigm and SHBSig, to improve the performance of neural networks and accurate results. Also, three new activation functions created with little variations in the DharaSig function named DharaSig1, DharaSig2 and DharaSig3. In this research study, variable numbers of hidden layers are tested with the variable number of neurons per hidden layer for the agriculture dataset. Variable values of momentum, seed and learning rate are also used in this study. Experiments show that newly created activation functions provide better results compared to ‘sigmoid’ default neural network activation function for agriculture datasets.

A Physics-Informed Neural Network (PINN) was developed to solve the complex Navier-Stokes (N-S) equations for multiphase flow measurement including flowrates of individual phases in the multiphase mixture, and phase ratios. The results were compared against a mathematical based multiphase flow measurement approach and validated through a controlled loop test using oil, water, and gas. The PINN embeds fundamental fluid dynamics principles into its learning process, ensuring that the neural network adheres to the governing physical laws of motion, continuity, and conservation. Unlike traditional neural networks that rely solely on data-driven learning, PINNs incorporate fluid dynamics driven differential equations, to enhance model accuracy and reliability. This study evaluates the accuracy, efficiency, and repeatability of PINNs by comparing their results against traditional mathematical-based multiphase flow measurement (MPFM) technology and controlled test cases. The developed PINN successfully solved the Navier- Stokes (N-S) equations in their closest approximation to the original form, with minimal assumptions and simplifications, to estimate multiphase flow rates, integrating fundamental fluid dynamics principles into its learning process. The results demonstrated that the PINN-based approach achieved accuracy comparable to traditional mathematical multiphase flow measurement (MPFM) technologies, while significantly improving computational efficiency. During controlled loop tests with oil, water, and gas, the PINN model consistently captured flow dynamics with high precision, validating its effectiveness under real-world conditions. Moreover, the PINN method exhibited strong generalization capabilities, adapting to various flow regimes without the need for extensive empirical calibration. Compared to conventional MPFM technologies, PINN reduced reliance on predefined correlations and offered greater adaptability to changing fluid properties. The repeatability of results confirmed the model's reliability, positioning PINNs as a promising alternative for complex multiphase flow measurement applications. These findings highlight the potential of PINNs as an innovative, physics-guided, and data-efficient solution, effectively bridging the gap between traditional physics-based methods and modern machine learning techniques. This paper presents an innovative application of Physics-Informed Neural Networks (PINNs) for multiphase flow measurement, offering a data-driven yet physics-guided alternative to traditional mathematical MPFM technologies. By embedding fundamental physical laws into the neural network training process, the proposed approach enhances accuracy, computational efficiency, and adaptability, while minimizing reliance on extensive empirical calibration. This advancement significantly improves real-time flow monitoring, equipping practicing engineers with a more reliable, data-efficient, and scalable solution for complex multiphase flow measurement in industrial applications.