In parallel with the continuously increasing parameter space dimensionality, search and optimization algorithms should support distributed parameter evaluations to reduce cumulative runtime. Intel's neuromorphic optimization library, Lava-Optimization, was introduced as an abstract optimization system compatible with neuromorphic systems developed in the broader Lava software framework. In this work, we introduce Lava Multi-Agent Optimization (LMAO) with native support for distributed parameter evaluations communicating with a central Bayesian optimization system. LMAO provides an abstract framework for deploying distributed optimization and search algorithms within the Lava software framework. Moreover, LMAO introduces support for random and grid search along with process connections across multiple levels of mathematical precision. We evaluate the algorithmic performance of LMAO with a traditional non-convex optimization problem, a fixed-precision transductive spiking graph neural network for citation graph classification, and a neuromorphic satellite scheduling problem. Our results highlight LMAO's efficient scaling to multiple processes, reducing cumulative runtime and minimizing the likelihood of converging to local optima.

Performing optimization with event-based asynchronous neuromorphic systems presents significant challenges. Intel’s neuromorphic computing framework, Lava, offers an abstract application programming interface designed for constructing event-based computational graphs. In this study, we introduce a novel framework tailored for asynchronous Bayesian optimization that is also compatible with Loihi 2. We showcase the capability of our asynchronous optimization framework by connecting it with a graph-based satellite scheduling problem running on physical Loihi 2 hardware.

Applications in robotics or other size-, weight- and power-constrained autonomous systems at the edge often require real-time and low-energy solutions to large optimization problems. Event-based and memory-integrated neuromorphic architectures promise to solve such optimization problems with superior energy efficiency and performance compared to conventional von Neumann architectures. Here, we present a method to solve convex continuous optimization problems with quadratic cost functions and linear constraints on Intel's scalable neuromorphic research chip Loihi 2. When applied to model predictive control (MPC) problems for the quadruped robotic platform ANYmal, this method achieves over two orders of magnitude reduction in combined energy-delay product compared to the state-of-the-art solver, OSQP, on (edge) CPUs and GPUs with solution times under ten milliseconds for various problem sizes. These results demonstrate the benefit of non-von-Neumann architectures for robotic control applications.

Applications in robotics or other size-, weight-, and power-constrained (SWaP) autonomous systems at the edge often require real-time and low-energy solutions to large optimization problems. Event-based and memory-integrated neuromorphic architectures promise to solve such optimization problems with superior energy efficiency and performance compared to conventional von Neumann architectures. Here, we present a method to solve convex continuous optimization problems with quadratic cost functions and linear constraints on Intel’s scalable neuromorphic research chip Loihi 2. When applied to model predictive control (MPC) problems for the quadruped robotic platform ANYmal, this method achieves more than two orders of magnitude reduction in the combined energy-delay product (EDP) compared to the state-of-the-art solver, OSQP, on (edge) CPUs and GPUs with solution times under 10 ms for various problem sizes. These results demonstrate the benefit of non-von Neumann architectures for robotic control applications.

When learning to perform motor tasks in a simulated environment, neural networks must be allowed to explore their action space to discover new potentially viable solutions. However, in an online learning scenario with physical hardware, this exploration must be constrained by relevant safety considerations in order to avoid damage to the agent's hardware and environment. We aim to address this problem by training a neural network, which we will refer to as a "safety network", to estimate the region of attraction (ROA) of a controlled autonomous dynamical system. This safety network can thereby be used to quantify the relative safety of proposed control actions and prevent the selection of damaging actions. Here we present our development of the safety network by training an artificial neural network (ANN) to represent the ROA of several autonomous dynamical system benchmark problems. The training of this network is predicated upon both Lyapunov theory and neural solutions to partial differential equations (PDEs). By learning to approximate the viscosity solution to a specially chosen PDE that contains the dynamics of the system of interest, the safety network learns to approximate a particular function, similar to a Lyapunov function, whose zero level set is boundary of the ROA. We train our safety network to solve these PDEs in a semi-supervised manner following a modified version of the Physics Informed Neural Network (PINN) approach, utilizing a loss function that penalizes disagreement with the PDE's initial and boundary conditions, as well as non-zero residual and variational terms. In future work we intend to apply this technique to reinforcement learning agents during motor learning tasks.

Graph neural networks have emerged as a specialized branch of deep learning, designed to address problems where pairwise relations between objects are crucial. Recent advancements utilize graph convolutional neural networks to extract features within graph structures. Despite promising results, these methods face challenges in real-world applications due to sparse features, resulting in inefficient resource utilization. Recent studies draw inspiration from the mammalian brain and employ spiking neural networks to model and learn graph structures. However, these approaches are limited to traditional Von Neumann-based computing systems, which still face hardware inefficiencies. In this study, we present a fully neuromorphic implementation of spiking graph neural networks designed for Loihi 2. We optimize network parameters using Lava Bayesian Optimization, a novel hyperparameter optimization system compatible with neuromorphic computing architectures. We showcase the performance benefits of combining neuromorphic Bayesian optimization with our approach for citation graph classification using fixed-precision spiking neurons. Our results demonstrate the capability of integer-precision, Loihi 2 compatible spiking neural networks in performing citation graph classification with comparable accuracy to existing floating point implementations.

Neuromorphic processors have garnered considerable interest in recent years for their potential in energy-efficient and high-speed computing. The Locally Competitive Algorithm (LCA) has been utilized for power efficient sparse coding on neuromorphic processors, including the first Loihi processor [4, 5]. With the Loihi 2 processor enabling custom neuron models and graded spike communication, more complex implementations of LCA are possible [9]. We present a new implementation of LCA designed for the Loihi 2 processor and perform an initial set of benchmarks comparing it to LCA on CPU and GPU devices. In these experiments LCA on Loihi 2 is orders of magnitude more efficient and faster for large sparsity penalties, while maintaining similar reconstruction quality. We find this performance improvement increases as the LCA parameters are tuned towards greater representation sparsity. Our study highlights the potential of neuromorphic processors, particularly Loihi 2, in enabling intelligent, autonomous, real-time processing on small robots, satellites where there are strict SWaP (small, lightweight, and low power) requirements. By demonstrating the superior performance of LCA on Loihi 2 compared to conventional computing device, our study suggests that Loihi 2 could be a valuable tool in advancing these types of applications. Overall, our study highlights the potential of neuromorphic processors for efficient and accurate data processing on resource-constrained devices.

Post-stroke emotional disturbances are common and distressing for the patients. Depression and anger are the two most common symptoms seen in post-stroke patients. These symptoms impact patient's life and the caregivers around them, leading to a poor and deteriorating life-style. Timely and efficient detection of such often unnoticed emotional disturbances can facilitate the recovery process through appropriate medication. A reliable, real-time, low power emotion recognition system on an edge device is considered highly desirable for the rehabilitation process of post-stroke patients. In this context, here we investigate a neuromorphic convolutional neural network (CNN) executed on Intel Loihi, to classify three emotional states: angry, happy and sad. The proposed neuromorphic solution (NC-Emotions) consumes only 0.96 W power to attain a near-state-of-the-art accuracy of 84.6% (SoTA is 86.2% on a GPU, consuming ∼35 W) at a real-time processing of 25 ms per frame which satisfies the typical frame arrival period of 33 ms. NC-Emotions model, therefore, provides a low-power, and real-time, edge-computing solution, suitable for domestic and clinical applications.

Though neuromorphic computers have typically targeted applications in machine learning and neuroscience (‘cognitive’ applications), they have many computational characteristics that are attractive for a wide variety of computational problems. In this work, we review the current state-of-the-art for non-cognitive applications on neuromorphic computers, including simple computational kernels for composition, graph algorithms, constrained optimization, and signal processing. We discuss the advantages of using neuromorphic computers for these different applications, as well as the challenges that still remain. The ultimate goal of this work is to bring awareness to this class of problems for neuromorphic systems to the broader community, particularly to encourage further work in this area and to make sure that these applications are considered in the design of future neuromorphic systems.

Deep artificial neural networks apply principles of the brain's information processing that led to breakthroughs in machine learning spanning many problem domains. Neuromorphic computing aims to take this a step further to chips more directly inspired by the form and function of biological neural circuits, so they can process new knowledge, adapt, behave, and learn in real time at low power levels. Despite several decades of research, until recently, very few published results have shown that today's neuromorphic chips can demonstrate quantitative computational value. This is now changing with the advent of Intel's Loihi, a neuromorphic research processor designed to support a broad range of spiking neural networks with sufficient scale, performance, and features to deliver competitive results compared to state-of-the-art contemporary computing architectures. This survey reviews results that are obtained to date with Loihi across the major algorithmic domains under study, including deep learning approaches and novel approaches that aim to more directly harness the key features of spike-based neuromorphic hardware. While conventional feedforward deep neural networks show modest if any benefit on Loihi, more brain-inspired networks using recurrence, precise spike-timing relationships, synaptic plasticity, stochasticity, and sparsity perform certain computation with orders of magnitude lower latency and energy compared to state-of-the-art conventional approaches. These compelling neuromorphic networks solve a diverse range of problems representative of brain-like computation, such as event-based data processing, adaptive control, constrained optimization, sparse feature regression, and graph search.

A short-ranged and time-varying attraction drives self-assembly of colloidal crystals from a suspension of colloidal spheres. Brownian dynamics simulations of this process demonstrate that the envelope for self-assembly of large, low defect crystals is broadened dramatically when this attractive interaction is switched on and off periodically in time. This process is termed dynamic self-assembly because temporal control of the inter-particle potential requires injection and extraction of energy from the self-assembling materials. We develop a theory using non-equilibrium statistical mechanics to determine the rate at which particles cross a similarly switched energy barrier, and show that there is a switching rate that maximizes barrier crossing. While barrier crossing towards thermodynamic equilibrium is limited by the Kramers hopping rate, the rate of out-of-equilibrium barrier crossing can exceed this limit. In the context of self-assembly, barrier crossing is the rate limiting step and responsible for both defect formation and slow nucleation. This simple theory is used to explain the optimal switching rate observed in our simulations of dynamic self-assembly. Dynamic self-assembly via switched potentials enables growth of ordered phases without thermodynamic constraints on the assembly kinetics.

We analyze the trajectory of suspended spherical particles moving through a square array of obstacles, in the deterministic limit and at zero Reynolds number. We show that in the dilute approximation of widely separated obstacles, the average motion of the particles is equivalent to the trajectory followed by a point particle moving through an array of obstacles with an effective radius. The effective radius accounts for the hydrodynamic as well as short-range repulsive nonhydrodynamic interactions between the suspended particles and the obstacles, and is equal to the critical offset at which particle trajectories become irreversible. Using this equivalent system we demonstrate the presence of directional locking in the trajectory of the particles and derive an inequality that accurately describes the "devil's staircase" type of structure observed in the migration angle as a function of the forcing direction. We use these results to determine the optimum resolution in the fractionation of binary mixtures using deterministic lateral-displacement microfluidic separation systems as well as to comment on the collision frequencies when the arrays of posts are utilized as immunocapture devices.

We present a computational investigation of the mechanism governing size-based particle separation in microfluidic pinched flow fractionation. We study the behavior of particles moving through a pinching gap (i.e., a constriction in the aperture of a channel) in the Stokes regime (negligible fluid and particle inertia) as a function of particle size. The constriction aperture is created by a plane wall and spherical obstacle, and emulates the pinching segment in pinched flow fractionation devices. The simulation results show that the distance of closest approach between the particle and obstacle surfaces (along a trajectory) decreases with increasing particle size. We then use the distance of closest approach to investigate the effect of short-range repulsive non-hydrodynamic interactions (e.g., solid-solid contact due to surface roughness, electrostatic, or steric repulsion, etc.). We define a critical trajectory as the one in which the minimum particle–obstacle separation is equal to the range of the non-hydrodynamic interactions. The results further show that the initial offset of the critical trajectory (defined as the critical offset) increases with particle size. We interpret the variation of the critical offset with particle size as the basis for size-based microfluidic separation in pinched flow fractionation. We also compare the effect of different driving fields on the particle trajectories; we simulate a constant force driving the particles in a quiescent fluid as well as a freely suspended particles in a pressure-driven flow. We observe that the particles approach closer to the obstacle when driven by a constant force, than those freely suspended in a pressure driven flow (for the same initial offset). On the other hand, the increment in the critical offset (as a function of particle size) is larger in the pressure-driven case than in the force-driven case. Thus, pressure-driven particle separation using pinched flow fractionation would prove more effective than its force-driven counterpart (e.g., particles settling under gravity through a pinching gap).

We present a numerical study of the effect that fluid and particle inertia have on the motion of suspended spherical particles through a geometric constriction to understand analogous microfluidic settings, such as pinched flow fractionation devices. The particles are driven by a constant force in a quiescent fluid, and the constriction (the pinching gap) corresponds to the space between a plane wall and a second, fixed sphere of the same size (the obstacle). The results show that, due to inertia and/or the presence of a geometric constriction the particles attain smaller separations to the obstacle. We then relate the minimum surface-to-surface separation to the effect that short-range, repulsive non-hydrodynamic interactions (such as solid-solid contact due to surface roughness, electrostatic double layer repulsion, etc.) would have on the particle trajectories. In particular, using a simple hard-core repulsive potential model for such interactions, we infer that the particles would experience larger lateral displacements moving through the pinching gap as inertia increases and/or the aperture of the constriction decreases. Thus, separation of particles based on differences in density is in principle possible, owing to the differences in inertia associated with them. We also discuss the case of significant inertia, in which the presence of a small construction may hinder separation by reducing inertia effects.

We investigate the motion of a suspended non-Brownian sphere past a fixed cylindrical or spherical obstacle in the limit of zero Reynolds number for arbitrary particle-obstacle aspect ratios. We consider both a suspended sphere moving in a quiescent fluid under the action of a uniform force as well as a uniform ambient velocity field driving a freely suspended particle. We determine the distribution of particles around a single obstacle and solve for the individual particle trajectories to comment on the transport of dilute suspensions past an array of fixed obstacles. First, we obtain an expression for the probability density function governing the distribution of a dilute suspension of particles around an isolated obstacle, and we show that it is isotropic. We then present an analytical expression -- derived using both Eulerian and Lagrangian approaches -- for the minimum particle-obstacle separation attained during the motion, as a function of the incoming impact parameter, i.e. the initial offset between the line of motion far from the obstacle and the coordinate axis parallel to the driving field. Further, we derive the asymptotic behaviour for small initial offsets and show that the minimum separation decays exponentially. Finally we use this analytical expression to define an effective hydrodynamic surface roughness based on the net lateral displacement experienced by a suspended sphere moving past an obstacle.

We investigate the settling of spherical particles through a pinching gap created by a cylindrical obstacle and a vertical wall. These macroscopic experiments capture the essence of pinched-flow-fractionation in microfluidics and highlight its deterministic nature. In the absence of pinching, we observe asymmetric trajectories consistent with a hard-core model of particle-obstacle repulsion that leads to separative lateral displacement. Then, we show that pinching promotes the onset of these short-range repulsion forces, amplifying the relative separation in the outgoing trajectory of different-size particles. Inertia effects, however, tend to reduce such relative separation and lead to a more complex behavior.