arXiv subjects

Morad Behandish

Publications and source records attributed to Morad Behandish.

At least 19 recordsLinked to original sources

arXiv2026

Interpretable Material Spatial Intelligence for Discovery of Governing Microstructural Features

Many material systems exhibit complex spatial and temporal interactions across multiple length scales and modalities that govern macroscopic behavior. Although Machine Learning (ML) is widely used in materials science to predict this behavior, most approaches still rely on handcrafted descriptors or aggregated representations that overlook spatial organization, limiting insight into governing mechanisms. We introduce Materials Spatial Intelligence (MSI), a framework inspired by spatial intelligence that learns directly from multimodal spatial observations of material systems. MSI encodes high-resolution microstructural and deformation data into shared latent representations that preserve spatial relationships while supporting property prediction, interpretation, and optimization. By combining multimodal representation learning, MSI identifies the key features governing mechanical behavior and property trade-offs in structural alloys. Beyond prediction, MSI enables feature-driven microstructure optimization and mechanism discovery. More broadly, MSI establishes a foundation for applying spatial intelligence to materials science, leveraging interpretable ML systems to accelerate scientific discovery and materiel design

cond-mat.mtrl-sci↗

arXiv2025

Co-design Optimization of Moving Parts for Compliance and Collision Avoidance

Design requirements for moving parts in mechanical assemblies are typically specified in terms of interactions with other parts. Some are purely kinematic (e.g., pairwise collision avoidance) while others depend on physics and material properties (e.g., deformation under loads). Kinematic design methods and physics-based shape/topology optimization (SO/TO) deal separately with these requirements. They rarely talk to each other as the former uses set algebra and group theory while the latter requires discretizing and solving differential equations. Hence, optimizing a moving part based on physics typically relies on either neglecting or pruning kinematic constraints in advance, e.g., by restricting the design domain to a collision-free space using an unsweep operation. In this paper, we show that TO can be used to co-design two or more parts in relative motion to simultaneously satisfy physics-based criteria and collision avoidance. We restrict our attention to maximizing linear-elastic stiffness while penalizing collision measures aggregated in time. We couple the TO loops for two parts in relative motion so that the evolution of each part's shape is accounted for when penalizing collision for the other part. The collision measures are computed by a correlation functional that can be discretized by left- and right-multiplying the shape design variables by a pre-computed matrix that depends solely on the motion. This decoupling is key to making the computations scalable for TO iterations. We demonstrate the effectiveness of the approach with 2D and 3D examples.

cs.RO↗

arXiv2024

Deep Neural Implicit Representation of Accessibility for Multi-Axis Manufacturing

One of the main concerns in design and process planning for multi-axis additive and subtractive manufacturing is collision avoidance between moving objects (e.g., tool assemblies) and stationary objects (e.g., a part unified with fixtures). The collision measure for various pairs of relative rigid translations and rotations between the two pointsets can be conceptualized by a compactly supported scalar field over the 6D non-Euclidean configuration space. Explicit representation and computation of this field is costly in both time and space. If we fix $O(m)$ sparsely sampled rotations (e.g., tool orientations), computation of the collision measure field as a convolution of indicator functions of the 3D pointsets over a uniform grid (i.e., voxelized geometry) of resolution $O(n^3)$ via fast Fourier transforms (FFTs) scales as in $O(mn^3 \log n)$ in time and $O(mn^3)$ in space. In this paper, we develop an implicit representation of the collision measure field via deep neural networks (DNNs). We show that our approach is able to accurately interpolate the collision measure from a sparse sampling of rotations, and can represent the collision measure field with a small memory footprint. Moreover, we show that this representation can be efficiently updated through fine-tuning to more efficiently train the network on multi-resolution data, as well as accommodate incremental changes to the geometry (such as might occur in iterative processes such as topology optimization of the part subject to CNC tool accessibility constraints).

cs.GR↗

arXiv2023

A multi-physics compiler for generating numerical solvers from differential equations

We develop a tool that enables domain experts to quickly generate numerical solvers for emerging multi-physics phenomena starting from a high-level description based on ordinary/partial differential equations and their initial and boundary conditions over a symbolic spacetime domain. This "multi-physics" compiler aims to bridge the gap between problem formulation and computation, which historically has spanned years or even decades. Specialized numerical solvers in areas such as computational fluid dynamics (CFD) often present a barrier to novice end users not well-versed in the intricacies of their underlying schemes, and requiring surgical modifications when coupling with additional physical components initially not accounted for by the solver. Through the use of an intermediate language that is neutral between classical and exterior calculus, the compiler generates correct-by-construction numerical source code that offers guarantees of immutable physical principles like conservation laws at the discrete level. We present a proof of concept for the multi-physics compiler through some examples involving compilation to OpenFOAM [1]. A specific use case that the compiler is well-suited for involves equation modification approaches, where the aim is to use simple numerical schemes such as central differencing through the additional of artificial terms to the original governing equations of the multi-physics problem [2, 3, 4].

physics.comp-ph↗

arXiv2023

A finite element method to compute the damping rate and frequency of oscillating fluids inside microfluidic nozzles

The computation of damping rates of an oscillating fluid with a free surface in which viscosity is small and surface tension high is numerically challenging. A typical application requiring such computation is drop-on-demand (DoD) microfluidic devices that eject liquid metal droplets, where accurate knowledge of damping rates for the least-damped oscillation modes following droplet ejection is paramount for assessing jetting stability at higher jetting frequencies. Computational fluid dynamics (CFD) simulations often struggle to accurately predict meniscus damping unless a very fine discretization is adopted, so calculations are computationally expensive. The faster alternative we adopt is to compute damping rates directly from the eigenvalues of the linearized problem. The surface tension term in Stokes or sloshing problems requires approximation of meniscus displacements, which introduces additional complexity in their numerical solution. We consider the combined effects of viscosity and surface tension, approximate the meniscus displacements, and construct a finite element method to compute the fluid's oscillation modes. We prove that the method is free of spurious modes with zero or positive damping rates, and we implement it with Taylor-Hood elements for velocity and pressure, and with continuous piecewise quadratic elements for meniscus displacement. We verify the numerical convergence of the method by reproducing the solution to an analytical benchmark problem and two more complex examples with axisymmetric geometry. We obtain the spatial shape and temporal evolution (angular frequency and damping rate) of the set of least-damped oscillation modes in minutes, compared to days for a CFD simulation. The method's ability to quickly generate accurate estimates of fluid oscillation damping rates makes it suitable for integration into design loops for prototyping microfluidic nozzles.

physics.comp-ph↗

arXiv2023

Model Consistency for Mechanical Design: Bridging Lumped and Distributed Parameter Models with A Priori Guarantees

Engineering design often involves representation in at least two levels of abstraction: the system-level, represented by lumped parameter models (LPMs), and the geometric-level, represented by distributed parameter models (DPMs). Functional design innovation commonly occurs at the system-level, followed by a geometric-level realization of functional LPM components. However, comparing these two levels in terms of behavioral outcomes can be challenging and time-consuming, leading to delays in design translations between system and mechanical engineers. In this paper, we propose a simulation-free scheme that compares LPMs and spatially-discretized DPMs based on their model specifications and behaviors of interest, regardless of modeling languages and numerical methods. We adopt a model order reduction (MOR) technique that a priori guarantees accuracy, stability, and convergence to improve the computational efficiency of large-scale models. Our approach is demonstrated through the model consistency analysis of several mechanical designs, showing its validity, efficiency, and generality. Our method provides a systematic way to compare system-level and geometric-level designs, improving reliability and facilitating design translation.

eess.SY↗

arXiv2023

Non-intrusive Hybrid Scheme for Multiscale Heat Transfer: Thermal Runaway in a Battery Pack

Accurate analytical and numerical modeling of multiscale systems is a daunting task. The need to properly resolve spatial and temporal scales spanning multiple orders of magnitude pushes the limits of both our theoretical models as well as our computational capabilities. Rigorous upscaling techniques enable efficient computation while bounding/tracking errors and helping to make informed cost-accuracy tradeoffs. The biggest challenges arise when the applicability conditions of upscaled models break down. Here, we present a non-intrusive two-way (iterative bottom-up top-down) coupled hybrid model, applied to thermal runaway in battery packs, that combines fine-scale and upscaled equations in the same numerical simulation to achieve predictive accuracy while limiting computational costs. First, we develop two methods with different orders of accuracy to enforce continuity at the coupling boundary. Then, we derive weak (i.e., variational) formulations of the fine-scale and upscaled governing equations for finite element (FE) discretization and numerical implementation in FEniCS. We demonstrate that hybrid simulations can accurately predict the average temperature fields within error bounds determined a priori by homogenization theory. Finally, we demonstrate the computational efficiency of the hybrid algorithm against fine-scale simulations.

math.NA↗

arXiv2023

Inverse asymptotic treatment: capturing discontinuities in fluid flows via equation modification

A major challenge in developing accurate and robust numerical solutions to multi-physics problems is to correctly model evolving discontinuities in field quantities, which manifest themselves as interfaces between different phases in multi-phase flows, or as shock and contact discontinuities in compressible flows. When a quick response is required to rapidly emerging challenges, the complexity of bespoke discretization schemes impedes a swift transition from problem formulation to computation, which is exacerbated by the need to compose multiple interacting physics. We introduce "inverse asymptotic treatment" (IAT) as a unified framework for capturing discontinuities in fluid flows that enables building directly computable models based on off-the-shelf numerics. By capturing discontinuities through modifications at the level of the governing equations, IAT can seamlessly handle additional physics and thus enable novice end users to quickly obtain numerical results for various multi-physics scenarios. We outline IAT in the context of phase-field modeling of two-phase incompressible flows, and then demonstrate its generality by showing how localized artificial diffusivity (LAD) methods for single-phase compressible flows can be viewed as instances of IAT. Through the real-world example of a laminar hypersonic compression corner, we illustrate IAT's ability to, within just a few months, generate a directly computable model whose wall metrics predictions for sufficiently small corner angles come close to that of NASA's VULKAN-CFD solver. Finally, we propose a novel LAD approach via "reverse-engineered" PDE modifications, inspired by total variation diminishing (TVD) flux limiters, to eliminate the problem-dependent parameter tuning that plagues traditional LAD. We demonstrate that, when combined with second-order central differencing, it can robustly and accurately model compressible flows.

physics.comp-ph↗

arXiv2022

Physics-Based Nozzle Design Rules for High-Frequency Liquid Metal Jetting

We present physics-based nozzle design rules to achieve high-throughput and stable jetting in drop-on-demand liquid metal 3D printing. The design rules are based on scaling laws that capture the change of meniscus oscillation relaxation time with geometric characteristics of the nozzle's inner profile. These characteristics include volume, cross-sectional area, and inner surface area of the nozzle. Using boundary layer theory for a simple geometry, we show that the meniscus settles faster when the ratio of inner surface area to volume is increased. High-fidelity multiphase flow simulations verify this scaling. We use these laws to explore several design concepts with parameterized classes of shapes that reduce the meniscus relaxation time while preserving desired droplet specs. Finally, we show that for various nozzle profile concepts, the optimal performance can be achieved by increasing the ratio of the circumferential surface area to the bulk volume to the extent that is allowable by manufacturing constraints.

physics.flu-dyn↗

arXiv2022

Hybrid Manufacturing Process Planning for Arbitrary Part and Tool Shapes

Hybrid manufacturing (HM) technologies combine additive and subtractive manufacturing (AM/SM) capabilities in multi-modal process plans that leverage the strengths of each. Despite the growing interest in HM technologies, software tools for process planning have not caught up with advances in hardware and typically impose restrictions that limit the design and manufacturing engineers' ability to systematically explore the full design and process planning spaces. We present a general framework for identifying AM/SM actions that make up an HM process plan based on accessibility and support requirements, using morphological operations that allow for arbitrary part and tool geometries to be considered. To take advantage of multi-modality, we define the actions to allow for temporary excessive material deposition or removal, with an understanding that subsequent actions can correct for them, unlike the case in unimodal (AM-only or SM-only) process plans that are monotonic. We use this framework to generate a combinatorial space of valid, potentially non-monotonic, process plans for a given part of arbitrary shape, a collection of AM/SM tools of arbitrary shapes, and a set of relative rotations (fixed for each action) between them, representing build/fixturing directions on $3-$axis machines. Finally, we use define a simple objective function quantifying the cost of materials and operating time in terms of deposition/removal volumes and use a search algorithm to explore the exponentially large space of valid process plans to find "cost-optimal" solutions. We demonstrate the effectiveness of our method on 3D examples.

cs.CG↗

arXiv2022

Co-generation of Collision-Free Shapes for Arbitrary One-Parametric Motion

Mechanical assemblies can exhibit complex relative motions, during which collisions between moving parts and their surroundings must be avoided. To define feasible design spaces for each part's shape, "maximal" collision-free pointsets can be computed using configuration space modeling techniques such as Minkowski operations and sweep/unsweep. For example, for a pair of parts undergoing a given relative motion, to make the problem well-posed, the geometry of one part (chosen arbitrarily) must be fixed to compute the maximal shape of the other part by an unsweep operation. Making such arbitrary choices in a multi-component assembly can place unnecessary restrictions on the design space. A broader family of collision-free pairs of parts can be explored, if fixing the geometry of a component is not required. In this paper, we formalize this family of collision-free shapes and introduce a generic method for generating a broad subset of them. Our procedure, which is an extension of the unsweep, allows for co-generation of a pair of geometries which are modified incrementally and simultaneously to avoid collision. We demonstrate the effectiveness and scalability of our procedure in both 2D and 3D by generating a variety of collision-free shapes. Notably, we show that our approach can automatically generate freeform cam and follower profiles, gear teeth, and screw threads, starting from colliding blocks of materials, solely from a specification of relative motion and without the use of any feature-informed heuristics. Moreover, our approach provides continuous measures of collision that can be incorporated into standard gradient-descent design optimization, allowing for simultaneous collision-free and physics-informed co-design of mechanical parts for assembly.

cs.CG↗

arXiv2022

FRC-TOuNN: Topology Optimization of Continuous Fiber Reinforced Composites using Neural Network

In this paper, we present a topology optimization (TO) framework to simultaneously optimize the matrix topology and fiber distribution of functionally graded continuous fiber-reinforced composites (FRC). Current approaches in density-based TO for FRC use the underlying finite element mesh both for analysis and design representation. This poses several limitations while enforcing sub-element fiber spacing and generating high-resolution continuous fibers. In contrast, we propose a mesh-independent representation based on a neural network (NN) both to capture the matrix topology and fiber distribution. The implicit NN-based representation enables geometric and material queries at a higher resolution than a mesh discretization. This leads to the accurate extraction of functionally-graded continuous fibers. Further, by integrating the finite element simulations into the NN computational framework, we can leverage automatic differentiation for end-to-end automated sensitivity analysis, i.e., we no longer need to manually derive cumbersome sensitivity expressions. We demonstrate the effectiveness and computational efficiency of the proposed method through several numerical examples involving various objective functions. We also show that the optimized continuous fiber reinforced composites can be directly fabricated at high resolution using additive manufacturing.

cs.CE↗

arXiv2022

Modeling of porous lithium metal electrodes: turning the Li-dendrite problem around

The properties of rechargeable lithium-ion batteries are determined by the electrochemical and kinetic properties of their constituent materials as well as by their underlying microstructure. Microstructural design can be leveraged to achieve a leap in performance and durability. Here we investigate a porous electrode structure, as a strategy to increase the surface area, and provide structural stability for Li-metal anodes. The porous architecture consists of a mixed electron/ion conductor that function as a scaffold for lithium metal deposition. A new finite element model was developed to simulate the large topological changes associated with Li plating/stripping. This model is used to predict the current density distribution as a function of material and structural properties. A dimensionless quantity that combines Li-ion conductivity, surface impedance and average pore size is shown to be a good indicator to predict the peak current density. Preventing current localization at the separator reduces the risk of cell shorting. The analyses show that the peak current scales as $(hG)^{1/2}$, where $h$ is the ratio between surface and bulk conductivity and $G$ is the average pore size. Stability analyses suggest that the growth is morphologically stable, and that confining Li-plating into pores can enable high-energy density solid-state batteries. In addition to optimizing porous electrodes design, this finite element method can be extended to studying other Li-battery structures.

cond-mat.mtrl-sci↗

arXiv2022

Surrogate Modeling for Physical Systems with Preserved Properties and Adjustable Tradeoffs

Determining the proper level of details to develop and solve physical models is usually difficult when one encounters new engineering problems. Such difficulty comes from how to balance the time (simulation cost) and accuracy for the physical model simulation afterwards. We propose a framework for automatic development of a family of surrogate models of physical systems that provide flexible cost-accuracy tradeoffs to assist making such determinations. We present both a model-based and a data-driven strategy to generate surrogate models. The former starts from a high-fidelity model generated from first principles and applies a bottom-up model order reduction (MOR) that preserves stability and convergence while providing a priori error bounds, although the resulting reduced-order model may lose its interpretability. The latter generates interpretable surrogate models by fitting artificial constitutive relations to a presupposed topological structure using experimental or simulation data. For the latter, we use Tonti diagrams to systematically produce differential equations from the assumed topological structure using algebraic topological semantics that are common to various lumped-parameter models (LPM). The parameter for the constitutive relations are estimated using standard system identification algorithms. Our framework is compatible with various spatial discretization schemes for distributed parameter models (DPM), and can supports solving engineering problems in different domains of physics.

cs.AI↗

arXiv2022

AI Research Associate for Early-Stage Scientific Discovery

Artificial intelligence (AI) has been increasingly applied in scientific activities for decades; however, it is still far from an insightful and trustworthy collaborator in the scientific process. Most existing AI methods are either too simplistic to be useful in real problems faced by scientists or too domain-specialized (even dogmatized), stifling transformative discoveries or paradigm shifts. We present an AI research associate for early-stage scientific discovery based on (a) a novel minimally-biased ontology for physics-based modeling that is context-aware, interpretable, and generalizable across classical and relativistic physics; (b) automatic search for viable and parsimonious hypotheses, represented at a high-level (via domain-agnostic constructs) with built-in invariants, e.g., postulated forms of conservation principles implied by a presupposed spacetime topology; and (c) automatic compilation of the enumerated hypotheses to domain-specific, interpretable, and trainable/testable tensor-based computation graphs to learn phenomenological relations, e.g., constitutive or material laws, from sparse (and possibly noisy) data sets.

cs.AI↗

arXiv2022

Accelerating Part-Scale Simulation in Liquid Metal Jet Additive Manufacturing via Operator Learning

Predicting part quality for additive manufacturing (AM) processes requires high-fidelity numerical simulation of partial differential equations (PDEs) governing process multiphysics on a scale of minimum manufacturable features. This makes part-scale predictions computationally demanding, especially when they require many small-scale simulations. We consider drop-on-demand liquid metal jetting (LMJ) as an illustrative example of such computational complexity. A model describing droplet coalescence for LMJ may include coupled incompressible fluid flow, heat transfer, and phase change equations. Numerically solving these equations becomes prohibitively expensive when simulating the build process for a full part consisting of thousands to millions of droplets. Reduced-order models (ROMs) based on neural networks (NN) or k-nearest neighbor (kNN) algorithms have been built to replace the original physics-based solver and are computationally tractable for part-level simulations. However, their quick inference capabilities often come at the expense of accuracy, robustness, and generalizability. We apply an operator learning (OL) approach to learn a mapping between initial and final states of the droplet coalescence process for enabling rapid and accurate part-scale build simulation. Preliminary results suggest that OL requires order-of-magnitude fewer data points than a kNN approach and is generalizable beyond the training set while achieving similar prediction error.

physics.flu-dyn↗

arXiv2021

PATO: Producibility-Aware Topology Optimization using Deep Learning for Metal Additive Manufacturing

In this paper, we propose PATO-a producibility-aware topology optimization (TO) framework to help efficiently explore the design space of components fabricated using metal additive manufacturing (AM), while ensuring manufacturability with respect to cracking. Specifically, parts fabricated through Laser Powder Bed Fusion are prone to defects such as warpage or cracking due to high residual stress values generated from the steep thermal gradients produced during the build process. Maturing the design for such parts and planning their fabrication can span months to years, often involving multiple handoffs between design and manufacturing engineers. PATO is based on the a priori discovery of crack-free designs, so that the optimized part can be built defect-free at the outset. To ensure that the design is crack free during optimization, producibility is explicitly encoded within the standard formulation of TO, using a crack index. Multiple crack indices are explored and using experimental validation, maximum shear strain index (MSSI) is shown to be an accurate crack index. Simulating the build process is a coupled, multi-physics computation and incorporating it in the TO loop can be computationally prohibitive. We leverage the current advances in deep convolutional neural networks and present a high-fidelity surrogate model based on an Attention-based U-Net architecture to predict the MSSI values as a spatially varying field over the part's domain. Further, we employ automatic differentiation to directly compute the gradient of maximum MSSI with respect to the input design variables and augment it with the performance-based sensitivity field to optimize the design while considering the trade-off between weight, manufacturability, and functionality. We demonstrate the effectiveness of the proposed method through benchmark studies in 3D as well as experimental validation.

cs.CE↗

arXiv2021

Topology Optimization for Manufacturing with Accessible Support Structures

Metal additive manufacturing (AM) processes often fabricate a near-net shape that includes the as-designed part as well as the sacrificial support structures that need to be machined away by subtractive manufacturing (SM), for instance multi-axis machining. Thus, although AM is capable of generating highly complex parts, the limitations of SM due to possible collision between the milling tool and the workpiece can render an optimized part non-manufacturable. We present a systematic approach to topology optimization (TO) of parts for AM followed by SM to ensure removability of support structures, while optimizing the part's performance. A central idea is to express the producibility of the part from the near-net shape in terms of accessibility of every support structure point using a given set of cutting tool assemblies and fixturing orientations. Our approach does not impose any artificial constraints on geometric complexity of the part, support structures, machining tools, and fixturing devices. We extend the notion of inaccessibility measure field (IMF) to support structures to identify the inaccessible points and capture their contributions to non-manufacturability by a continuous spatial field. IMF is then augmented to the sensitivity field to guide the TO towards a manufacturable design. The approach enables efficient and effective design space exploration by finding nontrivial complex designs whose near-net shape can be 3D printed and post-processed for support removal by machining with a custom set of tools and fixtures. We demonstrate the efficacy of our approach on nontrivial examples in 2D and 3D.

cs.CE↗